The document summarizes a lecture on equalization techniques for digital communications. It begins with the lecturer acknowledging feedback that previous lectures moved too quickly and were too technical. It then provides a high-level overview of equalization techniques, including:
- Zero-forcing equalization using linear filters and decision feedback equalizers
- MMSE equalization
- Fractionally spaced equalizers
It also summarizes the key concepts from previous lectures on digital transmission models and the optimal receiver structure involving a whitened matched filter front-end and maximum likelihood sequence estimation (MLSE). The goal of equalization techniques is to provide a lower complexity alternative to MLSE for the decision device while approaching similar performance with the use of channel coding
This document discusses model checking of time Petri nets (TPN). TPN extend ordinary Petri nets by associating time intervals with transitions, specifying minimum and maximum times for a transition to remain enabled before firing. The document outlines TPN semantics based on clocks or intervals, temporal logics like TCTL for specifying timed properties, and techniques for abstracting the generally infinite TPN state space into a finite representation to enable model checking of properties. Abstract states group markings by time variables and various abstractions aim to preserve linear or branching properties of the original state space.
This document contains instructions for completing several MATLAB tasks related to signal processing. It includes:
1. Generating an amplitude modulated (AM) signal and plotting its envelope.
2. Plotting sine waves and sampling a periodic signal at different frequencies.
3. Plotting a 2D Gaussian probability density function using different MATLAB plotting commands.
4. Normalizing and plotting a voltage signal defined by a given equation.
This document summarizes key aspects of designing an optimum receiver for binary data transmission presented in Chapter 5. It begins by representing signals using orthonormal basis functions to reduce the problem from waveforms to random variables. It then describes representing noise using a complete orthonormal set and how the noise coefficients are statistically independent Gaussian variables. Finally, it outlines how the optimum receiver works by projecting the received signal onto the basis functions, resulting in random variables that can be used for binary decision making to minimize the bit error probability.
Comparitive analysis of bit error rates of multiple input multiple output tra...slinpublishers
The document compares the bit error rates of multiple input multiple output (MIMO) transmission schemes, including spatial multiplexing, space-time block codes (STBC), and space-time block coded spatial modulation (STBC-SM). It finds that STBC-SM provides better performance than STBC and vertical-Bell labs layered space-time (V-BLAST) spatial multiplexing. Specifically, simulations show STBC-SM has a lower bit error rate than the other schemes when using four transmit and four receive antennas. The document explains the techniques of V-BLAST, STBC, and STBC-SM in detail.
A novel delay dictionary design for compressive sensing-based time varying ch...TELKOMNIKA JOURNAL
Compressive sensing (CS) is a new attractive technique adopted for Linear Time Varying channel estimation. orthogonal frequency division multiplexing (OFDM) was proposed to be used in 4G and 5G which supports high data rate requirements. Different pilot aided channel estimation techniques were proposed to better track the channel conditions, which consumes bandwidth, thus, considerable data rate reduced. In order to estimate the channel with minimum number of pilots, compressive sensing CS was proposed to efficiently estimate the channel variations. In this paper, a novel delay dictionary-based CS was designed and simulated to estimate the linear time varying (LTV) channel. The proposed dictionary shows the suitability of estimating the channel impulse response (CIR) with low to moderate Doppler frequency shifts with acceptable bit error rate (BER) performance.
The Fourier transform is a mathematical tool that transforms functions between the time and frequency domains. It breaks down any function or signal into the frequencies that make it up. This allows analysis of signals in the frequency domain, enabling applications like image and signal processing. The Fourier transform represents functions as a combination of sinusoidal functions like sines and cosines. The inverse Fourier transform reconstructs the original function from its frequency representation. Fourier transforms have many uses including solving differential equations, filtering sound and images, and analyzing signals like heartbeats.
This document discusses model checking of time Petri nets (TPN). TPN extend ordinary Petri nets by associating time intervals with transitions, specifying minimum and maximum times for a transition to remain enabled before firing. The document outlines TPN semantics based on clocks or intervals, temporal logics like TCTL for specifying timed properties, and techniques for abstracting the generally infinite TPN state space into a finite representation to enable model checking of properties. Abstract states group markings by time variables and various abstractions aim to preserve linear or branching properties of the original state space.
This document contains instructions for completing several MATLAB tasks related to signal processing. It includes:
1. Generating an amplitude modulated (AM) signal and plotting its envelope.
2. Plotting sine waves and sampling a periodic signal at different frequencies.
3. Plotting a 2D Gaussian probability density function using different MATLAB plotting commands.
4. Normalizing and plotting a voltage signal defined by a given equation.
This document summarizes key aspects of designing an optimum receiver for binary data transmission presented in Chapter 5. It begins by representing signals using orthonormal basis functions to reduce the problem from waveforms to random variables. It then describes representing noise using a complete orthonormal set and how the noise coefficients are statistically independent Gaussian variables. Finally, it outlines how the optimum receiver works by projecting the received signal onto the basis functions, resulting in random variables that can be used for binary decision making to minimize the bit error probability.
Comparitive analysis of bit error rates of multiple input multiple output tra...slinpublishers
The document compares the bit error rates of multiple input multiple output (MIMO) transmission schemes, including spatial multiplexing, space-time block codes (STBC), and space-time block coded spatial modulation (STBC-SM). It finds that STBC-SM provides better performance than STBC and vertical-Bell labs layered space-time (V-BLAST) spatial multiplexing. Specifically, simulations show STBC-SM has a lower bit error rate than the other schemes when using four transmit and four receive antennas. The document explains the techniques of V-BLAST, STBC, and STBC-SM in detail.
A novel delay dictionary design for compressive sensing-based time varying ch...TELKOMNIKA JOURNAL
Compressive sensing (CS) is a new attractive technique adopted for Linear Time Varying channel estimation. orthogonal frequency division multiplexing (OFDM) was proposed to be used in 4G and 5G which supports high data rate requirements. Different pilot aided channel estimation techniques were proposed to better track the channel conditions, which consumes bandwidth, thus, considerable data rate reduced. In order to estimate the channel with minimum number of pilots, compressive sensing CS was proposed to efficiently estimate the channel variations. In this paper, a novel delay dictionary-based CS was designed and simulated to estimate the linear time varying (LTV) channel. The proposed dictionary shows the suitability of estimating the channel impulse response (CIR) with low to moderate Doppler frequency shifts with acceptable bit error rate (BER) performance.
The Fourier transform is a mathematical tool that transforms functions between the time and frequency domains. It breaks down any function or signal into the frequencies that make it up. This allows analysis of signals in the frequency domain, enabling applications like image and signal processing. The Fourier transform represents functions as a combination of sinusoidal functions like sines and cosines. The inverse Fourier transform reconstructs the original function from its frequency representation. Fourier transforms have many uses including solving differential equations, filtering sound and images, and analyzing signals like heartbeats.
Analysis Predicted Location of Harmonic Distortion in RF Upconverter StructureTELKOMNIKA JOURNAL
A new mathematical analysis to predict the magnitude size of the distortion products from the
signal up-conversion process output is presented. The signal up-conversion process converts the digital
baseband from the analog baseband into a radio frequency signal. When the signal baseband involves
frequency offsetting then occurring a number of distortion products which can reduce the dynamic range
so it is difficult to meet the spectrum mask requirements within the operating band. This paper will focus on
methods of new mathematical analysis using a continuous frequency range and only applies to a single
side band tone, with constant amplitude into any value of frequency offsets. The novel contribution to the
analysis starts at generating the gate signal and convolution of the gate signal into the reference carrier
signal. The results show very close between the simulation results and the calculation of the predicted
location of the distortions.
Non-Uniform sampling and reconstruction of multi-band signalsmravendi
This document discusses non-uniform sampling and reconstruction of multi-band signals. It introduces a multi-band signal model and defines key terms like spectral support and occupancy. It then describes uniform sampling and why periodic non-uniform sampling is more efficient. The document outlines the sampling parameters, formulation, and reconstruction approach using a reduced order model. It provides an example and simulation results showing the original and reconstructed time and frequency domain signals. It also notes that reconstruction is possible even when each spectral cell is partly occupied.
This document provides an introduction to signals and systems. It defines signals as functions that represent information over time and gives examples such as sound waves and stock prices. Systems are defined as generators or transformers of signals. Signal processing involves manipulating signals to extract useful information, often by converting them to electrical forms. The document then classifies different types of signals such as continuous-time vs discrete-time, analog vs digital, deterministic vs random, and energy vs power signals. It also introduces some basic continuous-time signals like the unit step function, unit impulse function, and complex exponential signals.
SAMPLING & RECONSTRUCTION OF DISCRETE TIME SIGNALkaran sati
Discrete time signals can be obtained by sampling an analog signal at regular intervals or by observing an inherently discrete process. Sampling is the process of breaking a continuous signal into discrete samples by recording the signal's value at time intervals called the sampling period. According to the sampling theorem, a signal can be uniquely reconstructed from its samples if it is sampled at a rate greater than twice its highest frequency component. Reconstruction involves isolating the baseband spectrum from the spectral images caused by sampling through the use of a low-pass filter, which corresponds to convolving the samples with a sinc function. Practical reconstruction uses an approximation to the ideal sinc filter.
This document discusses optimal receivers for additive white Gaussian noise (AWGN) channels. It begins by modeling the digital communication system and channel as a vector channel with additive noise. It defines optimal receivers as those that minimize the error probability. The document then derives the maximum likelihood (ML) and maximum a posteriori probability (MAP) decision rules, and shows that the ML rule is to choose the message with highest probability density given the received vector. It also discusses estimating bits individually and relates bit and symbol error probabilities. Preprocessing is discussed, showing it cannot reduce the error rate of an optimal receiver.
The document discusses sampling theory and analog-to-digital conversion. It begins by explaining that most real-world signals are analog but must be converted to digital for processing. There are three steps: sampling, quantization, and coding. Sampling converts a continuous-time signal to a discrete-time signal by taking samples at regular intervals. The sampling theorem states that the sampling frequency must be at least twice the highest frequency of the sampled signal to avoid aliasing. Finally, it provides an example showing how to calculate the minimum sampling rate, or Nyquist rate, given the highest frequency of a signal.
(2013) Rigaud et al. - A parametric model and estimation techniques for the i...François Rigaud
This document proposes a parametric model to jointly model the inharmonicity and tuning of pianos across their entire pitch range. It uses a small number of parameters to represent both the specific design characteristics of different piano types and tuner practices. An estimation algorithm is presented that can estimate the parameters from recordings of isolated notes or chords, assuming the played notes are known. The model aims to provide a synthetic description of a particular piano's tuning/inharmonicity pattern that can highlight tuner choices and be useful for applications like piano synthesis or transcription of piano music.
This document proposes using a hybrid model and structured sparsity for under-determined convolutive audio source separation. It presents a mathematical model that combines a convex cost function with sparse regularization terms. A hybrid model is introduced using a union of two Gabor frames, each adapted to a different "morphological layer" of the signal. Structured sparsity is incorporated using a windowed group lasso operator to better exploit time-frequency structure. Experiments on speech and music mixtures show improved source separation performance compared to baseline methods, confirming the benefits of the proposed hybrid and structured sparsity approaches.
(2012) Rigaud, David, Daudet - Piano Sound Analysis Using Non-negative Matrix...François Rigaud
This document presents a method for estimating the tuning (fundamental frequency F0) and inharmonicity coefficient (B) of piano tones from single note or chord recordings. The method is based on non-negative matrix factorization with a parametric model for the dictionary atoms that includes the inharmonicity law as a relaxed constraint. The model is optimized using multiplicative update rules to estimate the parameters (B, F0) for each note, even in polyphonic recordings. Applications show the method can accurately estimate tuning and inharmonicity from single notes or chords.
(2011) Rigaud, David, Daudet - A Parametric Model of Piano TuningFrançois Rigaud
This document summarizes a parametric model of piano tuning that can generate tuning curves for an entire piano based on recordings of just a few isolated notes. It first introduces a 2-parameter model for the inharmonicity coefficient along the keyboard based on physical considerations of piano string design. It then proposes a 4-parameter model for the fundamental frequency evolution across the tessitura informed by tuning rules and accounting for the inharmonicity model. The overall model is shown to fit reference tuning data from 5 different pianos estimated from single note recordings, demonstrating its ability to approximate aural piano tuning across the instrument's range.
Vector space concepts can be used to represent energy signals. Any set of signals can be represented as linear combinations of orthogonal basis functions in an N-dimensional vector space. Each signal is determined by its vector of coefficients. This geometric representation in vector spaces allows defining properties like vector lengths, angles between vectors, and inner products. It provides a mathematical basis for analyzing signals and noise in communication systems.
(2012) Rigaud, Falaize, David, Daudet - Does Inharmonicity Improve an NMF-Bas...François Rigaud
This document investigates whether explicitly modeling inharmonicity improves piano transcription accuracy when using non-negative matrix factorization (NMF). It compares three models for the note spectra dictionary in NMF-based piano transcription: 1) strictly harmonic, 2) strictly following theoretical inharmonicity, and 3) relaxed inharmonicity constraints. Experimental results found the inharmonic models improved transcription accuracy compared to the harmonic model, but only when provided a good initialization. The paper aims to better understand how precisely a model needs to capture characteristics like inharmonicity for robust NMF analysis of piano recordings.
Zernike polynomials are used to simulate wavefront aberrations and produce interferograms. FFT and phase shifting techniques are used to analyze fringe patterns in interferograms to obtain phase information. However, the obtained phase is only determined up to a factor of 2π. Computer functions give a principal phase value between -π and π, but the actual phase map is continuous and requires adding an offset to unwrap the discontinuous phase distribution. This process of determining the continuous phase from the wrapped phase is called phase unwrapping.
Elaborato presentato durante l'esame di Calcolo Numerico (Magistrale Ing. Informatica).
Temi trattati:
- Trasformata di Fourier
- Trasformata dal continuo al discreto
- Integrazione numerica
- Discretizzazione con formula di quadratura
- Fast Fourier Transform
- Applicazione FFT in ambito biomedico per il rilevamento della frequenza cardiaca mediante sensore "MAX30100" prodotto dalla Maxim Integrated.
Blind channel estimation for mimo ofdm systemstrungquang0207
This document presents a blind channel estimation technique for MIMO-OFDM systems. It generalizes existing subspace-based methods for single-input single-output OFDM systems to operate with multiple transmit and receive antennas. The proposed method establishes conditions for channel identifiability. It obtains accurate channel estimates using a small number of OFDM symbols and is insensitive to overestimates of the true channel order. The method can work with no or insufficient cyclic prefix if virtual carriers are present, potentially increasing channel utilization. Simulation results show the mean-square error performance of the proposed method.
CSMA/CD is a media access control method used in early Ethernet technology that uses carrier sensing to detect other signals while transmitting. It improves on CSMA by terminating transmission as soon as a collision is detected to shorten the time before resending. There are three types of CSMA protocols: 1-Persistent, Non-Persistent, and P-Persistent. CSMA/CD networks can detect collisions within twice the propagation delay allowing aborted collisions. It was used in older Ethernet variants and is still supported for backwards compatibility.
This lecture covers signal and systems analysis, including:
1) Definitions of signals, systems, and their properties like time-invariance, linearity, stability, causality, and memory.
2) Classification of signals as continuous-time vs discrete-time, analog vs digital, deterministic vs random, periodic vs aperiodic.
3) Concepts of orthogonality, correlation, autocorrelation as they relate to signal comparison.
4) Review of the Fourier series and Fourier transform as tools to represent signals in the frequency domain.
This document discusses impulse response in signals and systems. It defines an impulse signal as having a value of zero except at t=0, where it has an infinitely high value. The impulse response describes the output of a system when given an impulse as input. It provides an example of finding the poles and zeros of a simple system transfer function. The document also derives the impulse response and step response of a first order system and explains the relationship between the two responses. Impulse response has applications in areas like loudspeakers, audio processing, and control systems.
This document summarizes a research paper that introduces a probabilistic model for analyzing line spectra, which are sets of prominent frequency components, in musical instrument sounds. The model assumes observations in a time frame are generated by a mixture of notes composed of partials and noise. For piano music specifically, the model introduces fundamental frequency and inharmonicity coefficient as parameters for each note that can be estimated from line spectra using an Expectation-Maximization algorithm. The paper applies this technique to unsupervised estimation of tuning and inharmonicity across the range of a piano from a recorded musical piece.
The document discusses the discrete Fourier transform (DFT) and its applications. It provides an overview of DFT and how it represents a signal in the frequency domain. It then describes the fast Fourier transform (FFT) algorithm, which efficiently computes the DFT. The document outlines algorithms to compute the inverse DFT and circular convolution using the DFT. It includes MATLAB code implementations of DFT, inverse DFT, FFT, and circular convolution. Graphs are shown comparing computation times of the algorithms.
The network layer performs three main functions:
1) Path determination to route packets from source to destination.
2) Switching to move packets through routers.
3) Call setup for some architectures that require establishing a path before data transmission.
1) The document describes a 6 band LED bargraph equalizer project created using an Analog Devices BF533 evaluation board.
2) It implements 6 bandpass filters to separate an audio input into frequency bands, applies gain adjustments to each band, and uses LEDs controlled by timers to display the output levels of each band.
3) Due to time constraints and issues adding the altered audio bands back together, the project achieved its basic functionality but had some unwanted frequencies and board performance problems.
Analysis Predicted Location of Harmonic Distortion in RF Upconverter StructureTELKOMNIKA JOURNAL
A new mathematical analysis to predict the magnitude size of the distortion products from the
signal up-conversion process output is presented. The signal up-conversion process converts the digital
baseband from the analog baseband into a radio frequency signal. When the signal baseband involves
frequency offsetting then occurring a number of distortion products which can reduce the dynamic range
so it is difficult to meet the spectrum mask requirements within the operating band. This paper will focus on
methods of new mathematical analysis using a continuous frequency range and only applies to a single
side band tone, with constant amplitude into any value of frequency offsets. The novel contribution to the
analysis starts at generating the gate signal and convolution of the gate signal into the reference carrier
signal. The results show very close between the simulation results and the calculation of the predicted
location of the distortions.
Non-Uniform sampling and reconstruction of multi-band signalsmravendi
This document discusses non-uniform sampling and reconstruction of multi-band signals. It introduces a multi-band signal model and defines key terms like spectral support and occupancy. It then describes uniform sampling and why periodic non-uniform sampling is more efficient. The document outlines the sampling parameters, formulation, and reconstruction approach using a reduced order model. It provides an example and simulation results showing the original and reconstructed time and frequency domain signals. It also notes that reconstruction is possible even when each spectral cell is partly occupied.
This document provides an introduction to signals and systems. It defines signals as functions that represent information over time and gives examples such as sound waves and stock prices. Systems are defined as generators or transformers of signals. Signal processing involves manipulating signals to extract useful information, often by converting them to electrical forms. The document then classifies different types of signals such as continuous-time vs discrete-time, analog vs digital, deterministic vs random, and energy vs power signals. It also introduces some basic continuous-time signals like the unit step function, unit impulse function, and complex exponential signals.
SAMPLING & RECONSTRUCTION OF DISCRETE TIME SIGNALkaran sati
Discrete time signals can be obtained by sampling an analog signal at regular intervals or by observing an inherently discrete process. Sampling is the process of breaking a continuous signal into discrete samples by recording the signal's value at time intervals called the sampling period. According to the sampling theorem, a signal can be uniquely reconstructed from its samples if it is sampled at a rate greater than twice its highest frequency component. Reconstruction involves isolating the baseband spectrum from the spectral images caused by sampling through the use of a low-pass filter, which corresponds to convolving the samples with a sinc function. Practical reconstruction uses an approximation to the ideal sinc filter.
This document discusses optimal receivers for additive white Gaussian noise (AWGN) channels. It begins by modeling the digital communication system and channel as a vector channel with additive noise. It defines optimal receivers as those that minimize the error probability. The document then derives the maximum likelihood (ML) and maximum a posteriori probability (MAP) decision rules, and shows that the ML rule is to choose the message with highest probability density given the received vector. It also discusses estimating bits individually and relates bit and symbol error probabilities. Preprocessing is discussed, showing it cannot reduce the error rate of an optimal receiver.
The document discusses sampling theory and analog-to-digital conversion. It begins by explaining that most real-world signals are analog but must be converted to digital for processing. There are three steps: sampling, quantization, and coding. Sampling converts a continuous-time signal to a discrete-time signal by taking samples at regular intervals. The sampling theorem states that the sampling frequency must be at least twice the highest frequency of the sampled signal to avoid aliasing. Finally, it provides an example showing how to calculate the minimum sampling rate, or Nyquist rate, given the highest frequency of a signal.
(2013) Rigaud et al. - A parametric model and estimation techniques for the i...François Rigaud
This document proposes a parametric model to jointly model the inharmonicity and tuning of pianos across their entire pitch range. It uses a small number of parameters to represent both the specific design characteristics of different piano types and tuner practices. An estimation algorithm is presented that can estimate the parameters from recordings of isolated notes or chords, assuming the played notes are known. The model aims to provide a synthetic description of a particular piano's tuning/inharmonicity pattern that can highlight tuner choices and be useful for applications like piano synthesis or transcription of piano music.
This document proposes using a hybrid model and structured sparsity for under-determined convolutive audio source separation. It presents a mathematical model that combines a convex cost function with sparse regularization terms. A hybrid model is introduced using a union of two Gabor frames, each adapted to a different "morphological layer" of the signal. Structured sparsity is incorporated using a windowed group lasso operator to better exploit time-frequency structure. Experiments on speech and music mixtures show improved source separation performance compared to baseline methods, confirming the benefits of the proposed hybrid and structured sparsity approaches.
(2012) Rigaud, David, Daudet - Piano Sound Analysis Using Non-negative Matrix...François Rigaud
This document presents a method for estimating the tuning (fundamental frequency F0) and inharmonicity coefficient (B) of piano tones from single note or chord recordings. The method is based on non-negative matrix factorization with a parametric model for the dictionary atoms that includes the inharmonicity law as a relaxed constraint. The model is optimized using multiplicative update rules to estimate the parameters (B, F0) for each note, even in polyphonic recordings. Applications show the method can accurately estimate tuning and inharmonicity from single notes or chords.
(2011) Rigaud, David, Daudet - A Parametric Model of Piano TuningFrançois Rigaud
This document summarizes a parametric model of piano tuning that can generate tuning curves for an entire piano based on recordings of just a few isolated notes. It first introduces a 2-parameter model for the inharmonicity coefficient along the keyboard based on physical considerations of piano string design. It then proposes a 4-parameter model for the fundamental frequency evolution across the tessitura informed by tuning rules and accounting for the inharmonicity model. The overall model is shown to fit reference tuning data from 5 different pianos estimated from single note recordings, demonstrating its ability to approximate aural piano tuning across the instrument's range.
Vector space concepts can be used to represent energy signals. Any set of signals can be represented as linear combinations of orthogonal basis functions in an N-dimensional vector space. Each signal is determined by its vector of coefficients. This geometric representation in vector spaces allows defining properties like vector lengths, angles between vectors, and inner products. It provides a mathematical basis for analyzing signals and noise in communication systems.
(2012) Rigaud, Falaize, David, Daudet - Does Inharmonicity Improve an NMF-Bas...François Rigaud
This document investigates whether explicitly modeling inharmonicity improves piano transcription accuracy when using non-negative matrix factorization (NMF). It compares three models for the note spectra dictionary in NMF-based piano transcription: 1) strictly harmonic, 2) strictly following theoretical inharmonicity, and 3) relaxed inharmonicity constraints. Experimental results found the inharmonic models improved transcription accuracy compared to the harmonic model, but only when provided a good initialization. The paper aims to better understand how precisely a model needs to capture characteristics like inharmonicity for robust NMF analysis of piano recordings.
Zernike polynomials are used to simulate wavefront aberrations and produce interferograms. FFT and phase shifting techniques are used to analyze fringe patterns in interferograms to obtain phase information. However, the obtained phase is only determined up to a factor of 2π. Computer functions give a principal phase value between -π and π, but the actual phase map is continuous and requires adding an offset to unwrap the discontinuous phase distribution. This process of determining the continuous phase from the wrapped phase is called phase unwrapping.
Elaborato presentato durante l'esame di Calcolo Numerico (Magistrale Ing. Informatica).
Temi trattati:
- Trasformata di Fourier
- Trasformata dal continuo al discreto
- Integrazione numerica
- Discretizzazione con formula di quadratura
- Fast Fourier Transform
- Applicazione FFT in ambito biomedico per il rilevamento della frequenza cardiaca mediante sensore "MAX30100" prodotto dalla Maxim Integrated.
Blind channel estimation for mimo ofdm systemstrungquang0207
This document presents a blind channel estimation technique for MIMO-OFDM systems. It generalizes existing subspace-based methods for single-input single-output OFDM systems to operate with multiple transmit and receive antennas. The proposed method establishes conditions for channel identifiability. It obtains accurate channel estimates using a small number of OFDM symbols and is insensitive to overestimates of the true channel order. The method can work with no or insufficient cyclic prefix if virtual carriers are present, potentially increasing channel utilization. Simulation results show the mean-square error performance of the proposed method.
CSMA/CD is a media access control method used in early Ethernet technology that uses carrier sensing to detect other signals while transmitting. It improves on CSMA by terminating transmission as soon as a collision is detected to shorten the time before resending. There are three types of CSMA protocols: 1-Persistent, Non-Persistent, and P-Persistent. CSMA/CD networks can detect collisions within twice the propagation delay allowing aborted collisions. It was used in older Ethernet variants and is still supported for backwards compatibility.
This lecture covers signal and systems analysis, including:
1) Definitions of signals, systems, and their properties like time-invariance, linearity, stability, causality, and memory.
2) Classification of signals as continuous-time vs discrete-time, analog vs digital, deterministic vs random, periodic vs aperiodic.
3) Concepts of orthogonality, correlation, autocorrelation as they relate to signal comparison.
4) Review of the Fourier series and Fourier transform as tools to represent signals in the frequency domain.
This document discusses impulse response in signals and systems. It defines an impulse signal as having a value of zero except at t=0, where it has an infinitely high value. The impulse response describes the output of a system when given an impulse as input. It provides an example of finding the poles and zeros of a simple system transfer function. The document also derives the impulse response and step response of a first order system and explains the relationship between the two responses. Impulse response has applications in areas like loudspeakers, audio processing, and control systems.
This document summarizes a research paper that introduces a probabilistic model for analyzing line spectra, which are sets of prominent frequency components, in musical instrument sounds. The model assumes observations in a time frame are generated by a mixture of notes composed of partials and noise. For piano music specifically, the model introduces fundamental frequency and inharmonicity coefficient as parameters for each note that can be estimated from line spectra using an Expectation-Maximization algorithm. The paper applies this technique to unsupervised estimation of tuning and inharmonicity across the range of a piano from a recorded musical piece.
The document discusses the discrete Fourier transform (DFT) and its applications. It provides an overview of DFT and how it represents a signal in the frequency domain. It then describes the fast Fourier transform (FFT) algorithm, which efficiently computes the DFT. The document outlines algorithms to compute the inverse DFT and circular convolution using the DFT. It includes MATLAB code implementations of DFT, inverse DFT, FFT, and circular convolution. Graphs are shown comparing computation times of the algorithms.
The network layer performs three main functions:
1) Path determination to route packets from source to destination.
2) Switching to move packets through routers.
3) Call setup for some architectures that require establishing a path before data transmission.
1) The document describes a 6 band LED bargraph equalizer project created using an Analog Devices BF533 evaluation board.
2) It implements 6 bandpass filters to separate an audio input into frequency bands, applies gain adjustments to each band, and uses LEDs controlled by timers to display the output levels of each band.
3) Due to time constraints and issues adding the altered audio bands back together, the project achieved its basic functionality but had some unwanted frequencies and board performance problems.
This document discusses different equalization techniques for DMT-based systems like ADSL. It begins with an overview of ADSL basics such as discrete multitone modulation and the need for equalization to combat channel distortion. It then describes the problem of equalizer design and various approaches that have been used, including current time-domain equalizers based on MMSE criteria and per-tone equalizers that optimize bit rate on a per-carrier basis. The document concludes by noting relationships between different equalizer designs and their underlying optimization problems.
The presentation discusses applications of the Hilbert transform in power engineering dynamics analysis. Specifically, it introduces the Hilbert transform and some of its interesting mathematical properties. It then discusses how the Hilbert transform can be used for modal analysis, identifying system damping and stability. Some challenges with using the Hilbert transform are noted, including complications that may arise from things like noise, missing data, and finite time windows. The presentation aims to provide an accessible introduction to the Hilbert transform and discuss its potential applications in power engineering signal processing and system identification.
This document discusses the purpose, benefits, and goals of the Biomedical Engineering (BME) program at Fairfield University. The BME program aims to leverage the university's network to connect students and academics to real-world commercial opportunities in medical technology. Its goals are to focus on entrepreneurship, bring together academic and industrial biomedical communities, and promote experiential education in product design, innovation, and entrepreneurship. The BME program offers multidisciplinary training and focuses on market needs and FDA regulations.
This document summarizes a presentation about equalizers for live sound use. It discusses the changing landscape of equalizer manufacturers and technologies. Key equalizer types - graphic and parametric - are described along with their characteristics. True response equalizers, which allow independent adjustment of frequency bands without interaction, are highlighted as an important development enabled by digital signal processing. Specific true response technologies from Behringer, Lake, and Rane are outlined. The document concludes with a discussion of new possibilities enabled by true response equalization.
This document provides information about the Computer Networks CR320 course. It lists the professor, Douglas Lyon, and his contact information. It states that the course text is Java for Programmers and provides a link to purchase it. Grading will be based one-third on a midterm exam, one-third on homework, and one-third on a final exam, both of which will be take-home exams. Students are asked to email the professor to be added to the course email list. The prerequisites are CS232 and MA172 or permission of the instructor, and students need a working knowledge of Java.
Crowdfunding allows entrepreneurs to raise money for new product development by posting their project online and taking pre-orders, with the goal of reaching a certain funding target within a set deadline. If the target is met, the backers' credit cards are charged and the entrepreneur uses the funds to produce and deliver the product. If the target is not met, no one is charged. The document provides tips for success, including making a prototype, producing a video, having production facilities lined up, gaining media coverage through blogs and social networks, and being persistent.
The document summarizes the origins and early history of digital computers. It describes how early calculating devices like the abacus led to mechanical calculators in the 16th-18th centuries. Charles Babbage designed the first general-purpose digital computers, the Difference Engine and Analytical Engine, in the 19th century. In the early 20th century, electro-mechanical machines and the concepts of stored programs and the binary system were developed. The first modern electronic digital computers were built during World War II to aid codebreaking efforts. After the war, the foundations of modern computing were established, including the stored-program architecture and transistor-based computers. Personal computers emerged in the 1970s due to declining costs of integrated circuits.
The document discusses medical image compression using the 3D Discrete Hartley Transform (DHT). It provides examples of applying the DHT to compress 3D X-ray angiography (XA) images and magnetic resonance (MR) brain images. Experiments showed that an XA image could be compressed with little loss of quality using a DHT with a quantization value of M=8. An MR brain image was effectively compressed using a DHT with M=2. The DHT provides an alternative transform to the Discrete Cosine Transform for lossy 3D medical image compression.
The document discusses advanced optimizations for computer memory hierarchies. It begins with an overview of the growing performance gap between processors and memory. Then, it describes 11 advanced cache optimizations for reducing cache hit times, miss penalties, and miss rates. These include techniques like small and simple caches, way prediction, trace caches, pipelined caches, non-blocking caches, compiler optimizations, and hardware prefetching. The document focuses on optimizations that aim to bridge the widening divide between processor and memory speeds.
This chapter discusses discrete image transforms. It introduces linear transformations and unitary transforms. The discrete Fourier transform (DFT) and discrete cosine transform (DCT) are presented as examples of unitary transforms. The DFT represents an image as a sum of sinusoidal basis images, while the DCT uses cosine basis images. Other transforms discussed include the discrete sine transform (DST), Hartley transform, and Hadamard transform. Orthogonal transforms preserve image properties while changing the representation basis.
This document provides an overview of Nvidia CUDA programming basics. It discusses the CUDA programming model, memory model, and API. The programming model describes how the GPU is seen as a compute device to execute kernels in parallel across a grid of thread blocks. Each block contains a batch of cooperating threads with shared memory. The memory model describes the different memory spaces including shared, global, and constant memory. The API extends C with qualifiers for functions, variables, and execution configurations to specify kernel execution. A simple example calculates scalar products across vectors in parallel. Optimization techniques for the example are discussed.
Inventors association of ct april 23 2013douglaslyon
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The document discusses Dijkstra's algorithm, a greedy algorithm for finding the shortest paths between nodes in a graph. It begins by introducing shortest path problems and comparing different algorithms like breadth-first search and Floyd's algorithm. It then describes Dijkstra's algorithm, which works by iteratively finding and settling the node with the smallest distance. The algorithm is proved to work using loop invariants. Its runtime is analyzed, showing it runs in O(m log n) time by using a priority queue like a binary heap. Dijkstra's algorithm is compared to Floyd's algorithm, with each being better depending on whether all paths or a single path is needed and on the graph density.
The document discusses TCP/IP (Transmission Control Protocol/Internet Protocol). TCP/IP provides networking services and protocols that allow for reliable data transmission between computers on a network like the Internet. It operates on a layered architecture with layers for network access, internetworking, and host-to-host transport. Key protocols include TCP, IP, and higher-level applications that use TCP/IP for network communication.
The document discusses CUDA memory types and optimization strategies for GPU programming. It describes the different memory spaces threads can access, including registers, shared memory, global memory, and constant memory. It recommends partitioning data into tiles that fit into the faster shared memory and loading tiles from global memory into shared memory to reuse data and reduce memory bandwidth usage. The document provides an example of tiled matrix multiplication on the GPU using this strategy with shared memory.
Fairfield univ lyons internet mktg 110315douglaslyon
This document provides guidance on marketing products on social media. It discusses how social media is becoming pervasive and important for businesses. Some key points made include:
- 80% of small businesses plan to increase their social media marketing. Being active can increase web traffic and search rankings.
- Many customers use social media to research purchases and are more likely to buy from businesses they connect with online.
- While you can sell on social media, it's better to drive traffic to your own website where you control sales and policies.
- Tips for social media marketing include sharing compelling content tailored to each platform's peak times, asking open-ended questions to generate discussion, and using it for customer support.
The document discusses Fourier transforms and their applications in signal processing. It provides examples of Fourier transforms of common signals like sine waves, delta functions, Gaussians, and square waves. It also examines how changing parameters of sampled signals like sampling rate and duration affect the Fourier transform and frequency resolution. The document demonstrates measuring multiple frequencies within a signal and discusses the discrete Fourier transform and fast Fourier transform which are used to analyze digital signals and images.
TOPdesk heeft gemerkt dat er veel vraag is naar een koppeling tussen TOPdesk en Microsoft System Center Operations Manager, ofwel MS SCOM. Vanuit deze gedachte is er een partnerschap ontstaan tussen TOPdesk en Microsoft-partner 3Fifty. TOPdesk heeft samen met deze partner een integratie gerealiseerd, die ervoor zorgt dat u in TOPdesk direct inzicht heeft in alerts vanuit uw ICT-infrastructuur. Een alert in SCOM wordt direct doorgezet als melding in TOPdesk.
Tijdens deze speciale themasessie vertellen wij u alles over de mogelijkheden van de TOPdesk-MS SCOM-integratie en is er een TOPdesk-consultant aanwezig die uw implementatievragen kan beantwoorden. Daarnaast verzorgt 3Fifty een live demonstratie omtrent de werking van deze koppeling. 20 november 2013
This document summarizes a lecture on equalization techniques for digital communications.
1) The optimal receiver structure for transmission over a channel consists of a whitened matched filter frontend and a maximum likelihood sequence estimator (MLSE) such as the Viterbi algorithm. However, the MLSE has high complexity.
2) Equalization filters combined with a memoryless decision device can provide a lower complexity alternative to the MLSE. Linear equalizers like zero-forcing and minimum mean squared error (MMSE) are discussed, as well as decision feedback equalizers.
3) The lecture reviews transmission models and optimal receivers developed in previous lectures, and establishes an input-output model of the transmission system to serve as the basis
This document summarizes a lecture on optimal receiver design for digital communication systems. It discusses different types of optimal receivers, including minimum bit-error rate (BER), maximum a-posteriori probability (MAP), maximum likelihood (ML), and minimum distance (MD) receivers. It also examines the receiver structures for transmitting a single symbol and a sequence of symbols over a linear channel with additive white Gaussian noise (AWGN). For a single symbol, the optimal receiver is a matched filter frontend followed by sampling at the symbol rate and decision device. For a sequence, a matched filter frontend and maximum likelihood sequence estimation (MLSE) are used.
This document summarizes a lecture on adaptive equalization. It discusses how equalizers can be designed when the channel is unknown or time-varying using training sequences. Specifically, it describes how training sequences can be used to identify the channel model and design an optimal linear equalizer using a least squares approach. This results in an equation to compute the optimal equalizer coefficients directly from the received training sequence samples. Similar approaches are described for fractionally spaced and decision feedback equalizers.
This document summarizes a lecture on transmitter design for digital communication systems. It discusses:
1) The basic components of a transmitter including constellations for linear modulation such as PAM, PSK, and QAM, and transmit filters.
2) Preliminaries on passband versus baseband transmission and how a baseband equivalent model can be obtained using complex envelope signals.
3) Details on common constellation designs including distance metrics for PAM, PSK, and QAM in an AWGN channel.
4) Analysis of bit error rate performance for the transmission of a single symbol over an AWGN channel for different constellations. The document also discusses designing transmit pulses to eliminate
This document summarizes a lecture on multi-tone modulation techniques. It discusses ADSL and VDSL specifications including spectrum allocation and channel characteristics. It then covers topics like bit loading, peak-to-average power ratio problems, time-domain equalization using a TEQ to shorten the channel impulse response, and alternative frequency-domain equalization structures. The document provides examples and illustrations of these concepts.
This document outlines a postacademic course on telecommunications transmission techniques taught by Marc Moonen at KU Leuven University. The course consists of 10 lectures covering basic digital communication principles as well as advanced topics like multicarrier modulation, CDMA, and MIMO transmission. It introduces concepts like modulation, channel coding, equalization, and multiple access. The document provides an overview of the course schedule, prerequisites, literature references and acknowledges prior work from which content has been adapted.
This document summarizes a lecture on smart antennas. It introduces the concept of spatial division multiple access (SDMA) which allows multiple users in the same cell to use the same frequency channel by using antenna arrays and signal processing. It describes early SDMA approaches that assumed line-of-sight propagation and used beamforming. More advanced approaches are needed to handle multipath propagation using techniques like MIMO channel modeling and source separation.
The document discusses Shannon's theory of channel capacity from 1948. It explains key information theory concepts like entropy, self-information, and mutual information. It then discusses the channel capacity of various channel models including frequency-flat and frequency-selective channels with additive white Gaussian noise. The maximum achievable transmission bit rate without error for a given channel is equal to the channel capacity, which depends on factors like bandwidth, signal-to-noise ratio, and optimal power allocation across frequencies for frequency-selective channels.
This document summarizes a lecture on CDMA (Code Division Multiple Access). It discusses different multiple access techniques including FDMA, TDMA, FH-CDMA, TH-CDMA and DS-CDMA. It provides details on DS-CDMA transmission and reception, including how code orthogonality allows multiple users to access the channel simultaneously. Advanced reception techniques for asynchronous CDMA and dispersive channels are also mentioned. Real-world CDMA applications including IS-95, UMTS and wireless LANs are listed.
The document discusses channel modeling and Kalman filter-based estimation for OFDM wireless communication systems. It provides an introduction to OFDM systems and outlines the channel modeling process, including modeling the channel as a multipath frequency selective fading channel using a tapped delay line. It also discusses implementing channel estimation using a Kalman filter and presenting results on simulating OFDM signal transmission through a Rayleigh fading channel. The goal is to accurately estimate the channel fading parameters using a joint time-frequency domain estimation model.
This document summarizes and compares different channel estimation techniques for OFDM systems. It discusses block-type pilot arrangement where pilots are sent on all subcarriers periodically, and comb-type pilot arrangement where pilots are spaced between data symbols. For block-type, channel estimation can be done with LS or MMSE. For comb-type, estimation is done at pilot frequencies using LS, MMSE or LMS, and interpolation between pilots with techniques like linear, cubic spline. Decision feedback equalizer is also implemented for block-type. Performance is evaluated using modulation schemes like QPSK, 16QAM under fading channels, and comb-type is shown to track fast fading better than block-type.
Introduction to Modulation and Demodulation.pptxNiharranjanAdit
1) The document discusses various modulation techniques used in communication systems including amplitude modulation (AM), frequency modulation (FM), phase modulation (PM), pulse amplitude modulation (PAM), frequency-shift keying (FSK), phase-shift keying (PSK), and their derivatives.
2) It explains the basic concepts of modulation such as using a message signal to control parameters of a carrier signal to transmit information.
3) Key modulation types covered are AM, which varies the amplitude of a carrier signal; FSK and PSK, which are used for digital modulation by shifting the frequency or phase of a carrier.
Spread spectrum communications and CDMAHossam Zein
This document discusses spread spectrum communications and CDMA. It provides an overview of spread spectrum techniques including direct sequence spread spectrum (DS/SS), frequency hopping, time hopping, and hybrid techniques. It explains that CDMA uses unique codes to allow multiple access. The document also discusses code properties like autocorrelation and cross-correlation, and code families including maximal length sequences, Gold codes, and Kasami codes that have good correlation properties for CDMA. It notes that correlation properties may be less important with more advanced receivers.
This document contains a syllabus for a Communication Electronics course. The syllabus covers 6 units:
1) Amplitude Modulation
2) Angle Modulation
3) Pulse Modulation
4) Noise
5) AM and FM Receivers
6) Broadband Communication Links and Multiplexing
The syllabus provides an overview of the key topics that will be covered in each unit, including the concepts, mathematical analysis, generation methods, and applications of various modulation techniques. It also lists recommended textbooks and reference books for the course.
Multi carrier equalization by restoration of redundanc y (merry) for adaptive...IJNSA Journal
This paper proposes a new blind adaptive channel shortening approach for multi-carrier systems. The
performance of the discrete Fourier transform-DMT (DFT-DMT) system is investigated with the proposed
DST-DMT system over the standard carrier serving area (CSA) loop1. Enhanced bit rates demonstrated
and less complexity also involved by the simulation of the DST-DMT system.
This document discusses analog communications and AM transmission. It provides an overview of the key components of an analog communication system including the source, transmitter, channel, receiver and recipient. It then discusses amplitude modulation techniques, including modulation index and the frequency spectrum of AM signals. It also covers AM receivers and transmitters, explaining common circuit stages like mixers, oscillators and modulators.
Iaetsd a novel scheduling algorithms for mimo based wireless networksIaetsd Iaetsd
This document proposes new scheduling algorithms for MIMO wireless networks to improve system performance. It discusses designing practical user scheduling algorithms to maximize capacity in MIMO systems. Various MAC scheduling policies are implemented and modified to provide distributed traffic control, robustness against interference, and increased efficiency of resource utilization. Simulations using MATLAB compare the different policies and draw important results and conclusions. The paper suggests new priority scheduling and partially fair scheduling algorithms incorporating awareness of interference to improve system-level performance in MIMO wireless networks.
The document discusses various modulation techniques including:
- Amplitude modulation (AM) which varies the amplitude of a carrier signal by a message signal. It results in double sideband modulation with upper and lower sidebands.
- Digital modulation techniques for binary signals including amplitude-shift keying (ASK), frequency-shift keying (FSK), and phase-shift keying (PSK).
- Multi-level modulation generalizes the above to multiple levels like quadrature phase-shift keying (QPSK).
- Pulse modulation techniques applied to a pulse train carrier including pulse amplitude modulation (PAM), pulse width modulation (PWM), and pulse position modulation (PPM).
The document discusses various modulation techniques including:
- Amplitude modulation (AM) which varies the amplitude of a carrier signal by a message signal. It results in double sideband modulation with upper and lower sidebands.
- Digital modulation techniques for binary signals including amplitude-shift keying (ASK), frequency-shift keying (FSK), and phase-shift keying (PSK).
- Multi-level modulation generalizes the above to multiple levels like quadrature phase-shift keying (QPSK) and M-ary modulation.
HCL Notes und Domino Lizenzkostenreduzierung in der Welt von DLAUpanagenda
Webinar Recording: https://www.panagenda.com/webinars/hcl-notes-und-domino-lizenzkostenreduzierung-in-der-welt-von-dlau/
DLAU und die Lizenzen nach dem CCB- und CCX-Modell sind für viele in der HCL-Community seit letztem Jahr ein heißes Thema. Als Notes- oder Domino-Kunde haben Sie vielleicht mit unerwartet hohen Benutzerzahlen und Lizenzgebühren zu kämpfen. Sie fragen sich vielleicht, wie diese neue Art der Lizenzierung funktioniert und welchen Nutzen sie Ihnen bringt. Vor allem wollen Sie sicherlich Ihr Budget einhalten und Kosten sparen, wo immer möglich. Das verstehen wir und wir möchten Ihnen dabei helfen!
Wir erklären Ihnen, wie Sie häufige Konfigurationsprobleme lösen können, die dazu führen können, dass mehr Benutzer gezählt werden als nötig, und wie Sie überflüssige oder ungenutzte Konten identifizieren und entfernen können, um Geld zu sparen. Es gibt auch einige Ansätze, die zu unnötigen Ausgaben führen können, z. B. wenn ein Personendokument anstelle eines Mail-Ins für geteilte Mailboxen verwendet wird. Wir zeigen Ihnen solche Fälle und deren Lösungen. Und natürlich erklären wir Ihnen das neue Lizenzmodell.
Nehmen Sie an diesem Webinar teil, bei dem HCL-Ambassador Marc Thomas und Gastredner Franz Walder Ihnen diese neue Welt näherbringen. Es vermittelt Ihnen die Tools und das Know-how, um den Überblick zu bewahren. Sie werden in der Lage sein, Ihre Kosten durch eine optimierte Domino-Konfiguration zu reduzieren und auch in Zukunft gering zu halten.
Diese Themen werden behandelt
- Reduzierung der Lizenzkosten durch Auffinden und Beheben von Fehlkonfigurationen und überflüssigen Konten
- Wie funktionieren CCB- und CCX-Lizenzen wirklich?
- Verstehen des DLAU-Tools und wie man es am besten nutzt
- Tipps für häufige Problembereiche, wie z. B. Team-Postfächer, Funktions-/Testbenutzer usw.
- Praxisbeispiele und Best Practices zum sofortigen Umsetzen
Main news related to the CCS TSI 2023 (2023/1695)Jakub Marek
An English 🇬🇧 translation of a presentation to the speech I gave about the main changes brought by CCS TSI 2023 at the biggest Czech conference on Communications and signalling systems on Railways, which was held in Clarion Hotel Olomouc from 7th to 9th November 2023 (konferenceszt.cz). Attended by around 500 participants and 200 on-line followers.
The original Czech 🇨🇿 version of the presentation can be found here: https://www.slideshare.net/slideshow/hlavni-novinky-souvisejici-s-ccs-tsi-2023-2023-1695/269688092 .
The videorecording (in Czech) from the presentation is available here: https://youtu.be/WzjJWm4IyPk?si=SImb06tuXGb30BEH .
Have you ever been confused by the myriad of choices offered by AWS for hosting a website or an API?
Lambda, Elastic Beanstalk, Lightsail, Amplify, S3 (and more!) can each host websites + APIs. But which one should we choose?
Which one is cheapest? Which one is fastest? Which one will scale to meet our needs?
Join me in this session as we dive into each AWS hosting service to determine which one is best for your scenario and explain why!
How to Get CNIC Information System with Paksim Ga.pptxdanishmna97
Pakdata Cf is a groundbreaking system designed to streamline and facilitate access to CNIC information. This innovative platform leverages advanced technology to provide users with efficient and secure access to their CNIC details.
Generating privacy-protected synthetic data using Secludy and MilvusZilliz
During this demo, the founders of Secludy will demonstrate how their system utilizes Milvus to store and manipulate embeddings for generating privacy-protected synthetic data. Their approach not only maintains the confidentiality of the original data but also enhances the utility and scalability of LLMs under privacy constraints. Attendees, including machine learning engineers, data scientists, and data managers, will witness first-hand how Secludy's integration with Milvus empowers organizations to harness the power of LLMs securely and efficiently.
Webinar: Designing a schema for a Data WarehouseFederico Razzoli
Are you new to data warehouses (DWH)? Do you need to check whether your data warehouse follows the best practices for a good design? In both cases, this webinar is for you.
A data warehouse is a central relational database that contains all measurements about a business or an organisation. This data comes from a variety of heterogeneous data sources, which includes databases of any type that back the applications used by the company, data files exported by some applications, or APIs provided by internal or external services.
But designing a data warehouse correctly is a hard task, which requires gathering information about the business processes that need to be analysed in the first place. These processes must be translated into so-called star schemas, which means, denormalised databases where each table represents a dimension or facts.
We will discuss these topics:
- How to gather information about a business;
- Understanding dictionaries and how to identify business entities;
- Dimensions and facts;
- Setting a table granularity;
- Types of facts;
- Types of dimensions;
- Snowflakes and how to avoid them;
- Expanding existing dimensions and facts.
How to Interpret Trends in the Kalyan Rajdhani Mix Chart.pdfChart Kalyan
A Mix Chart displays historical data of numbers in a graphical or tabular form. The Kalyan Rajdhani Mix Chart specifically shows the results of a sequence of numbers over different periods.
Unlock the Future of Search with MongoDB Atlas_ Vector Search Unleashed.pdfMalak Abu Hammad
Discover how MongoDB Atlas and vector search technology can revolutionize your application's search capabilities. This comprehensive presentation covers:
* What is Vector Search?
* Importance and benefits of vector search
* Practical use cases across various industries
* Step-by-step implementation guide
* Live demos with code snippets
* Enhancing LLM capabilities with vector search
* Best practices and optimization strategies
Perfect for developers, AI enthusiasts, and tech leaders. Learn how to leverage MongoDB Atlas to deliver highly relevant, context-aware search results, transforming your data retrieval process. Stay ahead in tech innovation and maximize the potential of your applications.
#MongoDB #VectorSearch #AI #SemanticSearch #TechInnovation #DataScience #LLM #MachineLearning #SearchTechnology
OpenID AuthZEN Interop Read Out - AuthorizationDavid Brossard
During Identiverse 2024 and EIC 2024, members of the OpenID AuthZEN WG got together and demoed their authorization endpoints conforming to the AuthZEN API
Monitoring and Managing Anomaly Detection on OpenShift.pdfTosin Akinosho
Monitoring and Managing Anomaly Detection on OpenShift
Overview
Dive into the world of anomaly detection on edge devices with our comprehensive hands-on tutorial. This SlideShare presentation will guide you through the entire process, from data collection and model training to edge deployment and real-time monitoring. Perfect for those looking to implement robust anomaly detection systems on resource-constrained IoT/edge devices.
Key Topics Covered
1. Introduction to Anomaly Detection
- Understand the fundamentals of anomaly detection and its importance in identifying unusual behavior or failures in systems.
2. Understanding Edge (IoT)
- Learn about edge computing and IoT, and how they enable real-time data processing and decision-making at the source.
3. What is ArgoCD?
- Discover ArgoCD, a declarative, GitOps continuous delivery tool for Kubernetes, and its role in deploying applications on edge devices.
4. Deployment Using ArgoCD for Edge Devices
- Step-by-step guide on deploying anomaly detection models on edge devices using ArgoCD.
5. Introduction to Apache Kafka and S3
- Explore Apache Kafka for real-time data streaming and Amazon S3 for scalable storage solutions.
6. Viewing Kafka Messages in the Data Lake
- Learn how to view and analyze Kafka messages stored in a data lake for better insights.
7. What is Prometheus?
- Get to know Prometheus, an open-source monitoring and alerting toolkit, and its application in monitoring edge devices.
8. Monitoring Application Metrics with Prometheus
- Detailed instructions on setting up Prometheus to monitor the performance and health of your anomaly detection system.
9. What is Camel K?
- Introduction to Camel K, a lightweight integration framework built on Apache Camel, designed for Kubernetes.
10. Configuring Camel K Integrations for Data Pipelines
- Learn how to configure Camel K for seamless data pipeline integrations in your anomaly detection workflow.
11. What is a Jupyter Notebook?
- Overview of Jupyter Notebooks, an open-source web application for creating and sharing documents with live code, equations, visualizations, and narrative text.
12. Jupyter Notebooks with Code Examples
- Hands-on examples and code snippets in Jupyter Notebooks to help you implement and test anomaly detection models.
Building Production Ready Search Pipelines with Spark and MilvusZilliz
Spark is the widely used ETL tool for processing, indexing and ingesting data to serving stack for search. Milvus is the production-ready open-source vector database. In this talk we will show how to use Spark to process unstructured data to extract vector representations, and push the vectors to Milvus vector database for search serving.
GraphRAG for Life Science to increase LLM accuracyTomaz Bratanic
GraphRAG for life science domain, where you retriever information from biomedical knowledge graphs using LLMs to increase the accuracy and performance of generated answers
GraphRAG for Life Science to increase LLM accuracy
Lecture5
1. Module-3 : Transmission
Lecture-5 (4/5/00)
Marc Moonen
Dept. E.E./ESAT, K.U.Leuven
marc.moonen@esat.kuleuven.ac.be
www.esat.kuleuven.ac.be/sista/~moonen/
Postacademic Course on
Telecommunications
Module-3 Transmission
Lecture-5 Equalization
Marc Moonen
K.U.Leuven/ESAT-SISTA
4/5/00
p. 1
2. Prelude
Comments on lectures being too fast/technical
* I assume comments are representative for (+/-)whole group
* Audience = always right, so some action needed….
To my own defense :-)
* Want to give an impression/summary of what today’s
transmission techniques are like (`box full of mathematics
& signal processing’, see Lecture-1).
Ex: GSM has channel identification (Lecture-6), Viterbi (Lecture-4),...
* Try & tell the story about the maths, i.o. math. derivation.
* Compare with textbooks, consult with colleagues working in
transmission...
Postacademic Course on
Telecommunications
Module-3 Transmission
Lecture-5 Equalization
Marc Moonen
K.U.Leuven-ESAT/SISTA
4/5/00
p. 2
3. Prelude
Good news
* New start (I): Will summarize Lectures (1-2-)3-4.
-only 6 formulas* New start (II) : Starting point for Lectures 5-6 is 1 (simple)
input-output model/formula (for Tx+channel+Rx).
* Lectures 3-4-5-6 = basic dig.comms principles, from then
on focus on specific systems, DMT (e.g. ADSL), CDMA
(e.g. 3G mobile), ...
Bad news :
* Some formulas left (transmission without formulas = fraud)
* Need your effort !
* Be specific about the further (math) problems you may have.
Postacademic Course on
Telecommunications
Module-3 Transmission
Lecture-5 Equalization
Marc Moonen
K.U.Leuven-ESAT/SISTA
4/5/00
p. 3
4. Lecture-5 : Equalization
Problem Statement :
• Optimal receiver structure consists of
* Whitened Matched Filter (WMF) front-end
(= matched filter + symbol-rate sampler + `pre-cursor
equalizer’ filter)
* Maximum Likelihood Sequence Estimator (MLSE),
(instead of simple memory-less decision device)
• Problem: Complexity of Viterbi Algorithm (MLSE)
• Solution: Use equalization filter + memory-less
decision device (instead of MLSE)...
Postacademic Course on
Telecommunications
Module-3 Transmission
Lecture-5 Equalization
Marc Moonen
K.U.Leuven-ESAT/SISTA
4/5/00
p. 4
5. Lecture-5: Equalization - Overview
• Summary of Lectures (1-2-)3-4
Transmission of 1 symbol :
Matched Filter (MF) front-end
Transmission of a symbol sequence :
Whitened Matched Filter (WMF) front-end & MLSE (Viterbi)
• Zero-forcing Equalization
Linear filters
Decision feedback equalizers
• MMSE Equalization
• Fractionally Spaced Equalizers
Postacademic Course on
Telecommunications
Module-3 Transmission
Lecture-5 Equalization
Marc Moonen
K.U.Leuven-ESAT/SISTA
4/5/00
p. 5
6. Summary of Lectures (1-2-)3-4
Channel Model:
ak (symbols)
ˆ
ak
h(t)
?
transmitter
+
n(t)
AWGN
channel
...
?
receiver (to be defined)
Continuous-time channel
=Linear filter channel + additive white Gaussian noise (AWGN)
Postacademic Course on
Telecommunications
Module-3 Transmission
Lecture-5 Equalization
Marc Moonen
K.U.Leuven-ESAT/SISTA
4/5/00
p. 6
7. Summary of Lectures (1-2-)3-4
Transmitter:
r(t)
s(t)
ˆ
ak
ak . Es
p(t)
h(t)
...
transmit
pulse
transmitter
+
n(t)
AWGN
channel
?
receiver (to be defined)
* Constellations (linear modulation):
n bits -> 1 symbol a k (PAM/QAM/PSK/..)
* Transmit filter p(t) :
s(t )
Es .
ak . p(t kTs )
k
Postacademic Course on
Telecommunications
Module-3 Transmission
Lecture-5 Equalization
Marc Moonen
K.U.Leuven-ESAT/SISTA
4/5/00
p. 7
8. Summary of Lectures (1-2-)3-4
p(t)
Transmitter:
t
s(t)
Example
ak . Es
t
p(t)
discrete-time
symbol sequence
transmit
pulse
continuous-time
transmit signal
transmitter
-> piecewise constant p(t) (`sample & hold’) gives s(t) with
infinite bandwidth, so not the greatest choice for p(t)..
-> p(t) usually chosen as a (perfect) low-pass filter (e.g. RRC)
Postacademic Course on
Telecommunications
Module-3 Transmission
Lecture-5 Equalization
Marc Moonen
K.U.Leuven-ESAT/SISTA
4/5/00
p. 8
9. Summary of Lectures (1-2-)3-4
Receiver:
In Lecture-3, a receiver structure was postulated (front-end
filter + symbol-rate sampler + memory-less decision
device). For transmission of 1 symbol, it was found that the
front-end filter should be `matched’ to the received pulse.
a0 . Es
p(t)
h(t)
transmit
pulse
transmitter
Postacademic Course on
Telecommunications
1/Ts
+
n(t)
AWGN
channel
Module-3 Transmission
Lecture-5 Equalization
front-end
filter
u0
ˆ
a0
receiver
Marc Moonen
K.U.Leuven-ESAT/SISTA
4/5/00
p. 9
10. Summary of Lectures (1-2-)3-4
Receiver: In Lecture-4, optimal receiver design was
based on a minimum distance criterion :
min a0 ,a1 ,...,aK | r (t )
ˆ ˆ
ˆ
ˆ
ak . p' (t kTs ) |2 dt
Es .
k
• Transmitted signal is
• Received signal
s(t )
Es .
ak . p(t kTs )
k
r (t )
Es .
ak . p' (t kTs ) n(t )
k
• p’(t)=p(t)*h(t)=transmitted pulse, filtered by channel
Postacademic Course on
Telecommunications
Module-3 Transmission
Lecture-5 Equalization
Marc Moonen
K.U.Leuven-ESAT/SISTA
4/5/00
p. 10
11. Summary of Lectures (1-2-)3-4
Receiver: In Lecture-4, it was found that for transmission
of 1 symbol, the receiver structure of Lecture 3 is indeed
optimal !
min a0 u0
ˆ
p’(t)=p(t)*h(t)
sample at t=0
a0 . Es
p(t)
h(t)
transmit
pulse
transmitter
Postacademic Course on
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ˆ
( Es .g 0 ).a0
2
+
n(t)
AWGN
channel
Module-3 Transmission
Lecture-5 Equalization
1/Ts
p’(-t)*
u0
front-end
filter
ˆ
a0
receiver
Marc Moonen
K.U.Leuven-ESAT/SISTA
4/5/00
p. 11
12. Summary of Lectures (1-2-)3-4
• Receiver: For transmission of a symbol sequence, the
optimal receiver structure is...
K
K
Es .
k 1 l 1
ak . Es
p(t)
h(t)
transmit
pulse
transmitter
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+
n(t)
AWGN
channel
Module-3 Transmission
Lecture-5 Equalization
2
ˆ*
ak .uk
uk
min a0 ,...,aK
ˆ
ˆ
ˆ*
ˆ
ak .g k l .al
K
ˆ
ak
k 1
1/Ts
p’(-t)*
front-end
filter
receiver
sample at t=k.Ts
Marc Moonen
K.U.Leuven-ESAT/SISTA
4/5/00
p. 12
13. Summary of Lectures (1-2-)3-4
Receiver:
• This receiver structure is remarkable, for it is
based on symbol-rate sampling (=usually below
Nyquist-rate sampling), which appears to be
allowable if preceded by a matched-filter front-end.
• Criterion for decision device is too complicated.
Need for a simpler criterion/procedure...
Postacademic Course on
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Module-3 Transmission
Lecture-5 Equalization
Marc Moonen
K.U.Leuven-ESAT/SISTA
4/5/00
p. 13
14. Summary of Lectures (1-2-)3-4
Receiver: 1st simplification by insertion of an additional
(magic) filter (after sampler).
* Filter = `pre-cursor equalizer’ (see below)
* Complete front-end = `Whitened matched filter’
K
min a0 ,...,aK
ˆ
ˆ
K
ym
m 1
2
ˆ
ak .hm
k
k 1
uk
ak . Es
p(t)
transmit
pulse
transmitter
Postacademic Course on
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h(t)
+
n(t)
AWGN
channel
1/Ts
p’(-t)*
front-end
filter
Module-3 Transmission
Lecture-5 Equalization
yk
ˆ
ak
1/L*(1/z*)
receiver
Marc Moonen
K.U.Leuven-ESAT/SISTA
4/5/00
p. 14
15. Summary of Lectures (1-2-)3-4
Receiver: The additional filter is `magic’ in that it turns the
complete transmitter-receiver chain into a simple inputoutput model:
yk
h0 .ak
h1..ak
h2 ..ak
yk
(h0 h1.z 1 h2 .z 2 h3 .z 3 ...).ak
1
2
h3 .ak
3
... wk
wk
H (z)
uk
ak . Es
p(t)
transmit
pulse
h(t)
1/Ts
p’(-t)*
front-end
n(t)
filter
ˆ
ak
+
AWGN
transmitter channel
Postacademic Course on
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yk
Module-3 Transmission
Lecture-5 Equalization
1/L*(1/z*)
receiver
Marc Moonen
K.U.Leuven-ESAT/SISTA
4/5/00
p. 15
16. Summary of Lectures (1-2-)3-4
Receiver: The additional filter is `magic’ in that it turns the
complete transmitter-receiver chain into a simple inputoutput model:
yk
h0 .ak
h1.ak
1
h2 .ak
2
h3 .ak
3
... wk
wk = additive white Gaussian noise
means interference from future
(`pre-cursor) symbols has been cancelled, hence only
interference from past (`post-cursor’) symbols remains
h1
h
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2
... 0
Module-3 Transmission
Lecture-5 Equalization
Marc Moonen
K.U.Leuven-ESAT/SISTA
4/5/00
p. 16
17. Summary of Lectures (1-2-)3-4
Receiver: Based on the input-output model
yk
h0 .ak
h1..ak
h2 ..ak
1
2
h3 .ak
3
... wk
one can compute the transmitted symbol sequence as
K
min a0 ,...,aK
ˆ
ˆ
K
ym
m 1
2
ˆ
ak .hm
k
k 1
A recursive procedure for this = Viterbi Algorithm
Problem = complexity proportional to M^N !
(N=channel-length=number of non-zero taps in H(z) )
Postacademic Course on
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Module-3 Transmission
Lecture-5 Equalization
Marc Moonen
K.U.Leuven-ESAT/SISTA
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p. 17
18. Problem statement (revisited)
• Cheap alternative for MLSE/Viterbi ?
• Solution: equalization filter + memory-less
decision device (`slicer’)
Linear filters
Non-linear filters (decision feedback)
• Complexity : linear in number filter taps
• Performance : with channel coding, approaches
MLSE performance
Postacademic Course on
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Module-3 Transmission
Lecture-5 Equalization
Marc Moonen
K.U.Leuven-ESAT/SISTA
4/5/00
p. 18
19. Preliminaries (I)
• Our starting point will be the input-output model for
transmitter + channel + receiver whitened matched filter
front-end
yk
h0 .ak
h1.ak
1
h2 .ak
ak
ak
h0
h1
2
h3 .ak
ak
1
h2
2
3
... wk
ak
h3
wk
Postacademic Course on
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3
yk
Module-3 Transmission
Lecture-5 Equalization
Marc Moonen
K.U.Leuven-ESAT/SISTA
4/5/00
p. 19
20. Preliminaries (II)
• PS: z-transform is `shorthand notation’ for discrete-time
signals…
A( z )
ai .z
i
a0 .z
0
a1.z
1
a2 . z
2
....
h0 .z
0
h1.z
1
h2 .z
2
....
i 0
H ( z)
hi .z
i
i 0
…and for input/output behavior of discrete-time systems
yk
h0 .ak
h1.ak
1
h2 .ak
hence
Y ( z ) H ( z ).A( z ) W ( z )
Postacademic Course on
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Module-3 Transmission
Lecture-5 Equalization
2
h3 .ak
A(z )
3
... wk
Y (z )
H(z)
W (z )
Marc Moonen
K.U.Leuven-ESAT/SISTA
4/5/00
p. 20
21. Preliminaries (III)
• PS: if a different receiver front-end is used (e.g. MF
instead of WMF, or …), a similar model holds
yk
~
... h 2 .ak
2
~
h 1.ak
1
~
~
h0 .ak h1.ak
1
~
h2 .ak
2
~
... wk
for which equalizers can be designed in a similar fashion...
Postacademic Course on
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Module-3 Transmission
Lecture-5 Equalization
Marc Moonen
K.U.Leuven-ESAT/SISTA
4/5/00
p. 21
22. Preliminaries (IV)
PS: properties/advantages of the WMF front end
• additive noise wk = white (colored in general model)
• H(z) does not have anti-causal taps h 1 h 2 ... 0
pps: anti-causal taps originate, e.g., from transmit filter design (RRC,
etc.). practical implementation based on causal filters + delays...
• H(z) `minimum-phase’ :
1
=`stable’ zeroes, hence (causal) inverse H ( z ) exists &
stable
= energy of the impulse response maximally concentrated
in the early samples
Postacademic Course on
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Module-3 Transmission
Lecture-5 Equalization
Marc Moonen
K.U.Leuven-ESAT/SISTA
4/5/00
p. 22
23. Preliminaries (V)
yk
h0 .ak
h1.ak 1 h2 .ak 2 h3 .ak 3 ...
wk
ISI
NOISE
• `Equalization’: compensate for channel distortion.
Resulting signal fed into memory-less decision device.
• In this Lecture :
- channel distortion model assumed to be known
- no constraints on the complexity of the
equalization filter (number of filter taps)
• Assumptions relaxed in Lecture 6
Postacademic Course on
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Module-3 Transmission
Lecture-5 Equalization
Marc Moonen
K.U.Leuven-ESAT/SISTA
4/5/00
p. 23
24. Zero-forcing & MMSE Equalizers
yk
h0 .ak
h1.ak 1 h2 .ak 2 h3 .ak 3 ...
wk
ISI
NOISE
2 classes :
Zero-forcing (ZF) equalizers
eliminate inter-symbol-interference (ISI) at the
slicer input
Minimum mean-square error (MMSE) equalizers
tradeoff between minimizing ISI and minimizing
noise at the slicer input
Postacademic Course on
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Module-3 Transmission
Lecture-5 Equalization
Marc Moonen
K.U.Leuven-ESAT/SISTA
4/5/00
p. 24
25. Zero-forcing Equalizers
Zero-forcing Linear Equalizer (LE) :
- equalization filter is inverse of H(z)
- decision device (`slicer’)
C ( z)
A(z )
H 1 ( z)
ˆ
A( z )
Y (z )
C(z)
H(z)
W (z )
• Problem : noise enhancement ( C(z).W(z) large)
Postacademic Course on
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Module-3 Transmission
Lecture-5 Equalization
Marc Moonen
K.U.Leuven-ESAT/SISTA
4/5/00
p. 25
26. Zero-forcing Equalizers
Zero-forcing Linear Equalizer (LE) :
- ps: under the constraint of zero-ISI at the slicer
input, the LE with whitened matched filter front-end
is optimal in that it minimizes the noise at the slicer
input
- pps: if a different front-end is used, H(z) may have
unstable zeros (non-minimum-phase), hence may
be `difficult’ to invert.
Postacademic Course on
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Module-3 Transmission
Lecture-5 Equalization
Marc Moonen
K.U.Leuven-ESAT/SISTA
4/5/00
p. 26
27. Zero-forcing Equalizers
Zero-forcing Non-linear Equalizer
Decision Feedback Equalization (DFE) :
- derivation based on `alternative’ inverse of H(z) :
A(z )
ˆ
A( z )
Y (z )
H(z)
W (z )
1-H(z)
(ps: this is possible if H(z) has h0 1
another property of the WMF model)
, which is
- now move slicer inside the feedback loop :
Postacademic Course on
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Module-3 Transmission
Lecture-5 Equalization
Marc Moonen
K.U.Leuven-ESAT/SISTA
4/5/00
p. 27
28. Zero-forcing Equalizers
A(z )
Y (z )
ˆ
A( z )
H(z)
W (z )
D(z)
D( z ) 1 H ( z )
moving slicer inside the feedback loop has…
- beneficial effect on noise: noise is removed that
would otherwise circulate back through the loop
- beneficial effect on stability of the feedback loop:
output of the slicer is always bounded, hence
feedback loop always stable
Performance intermediate between MLSE and linear equaliz.
Postacademic Course on
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Module-3 Transmission
Lecture-5 Equalization
Marc Moonen
K.U.Leuven-ESAT/SISTA
4/5/00
p. 28
29. Zero-forcing Equalizers
Decision Feedback equalization (DFE) :
- general DFE structure
C(z): `pre-cursor’ equalizer
(eliminates ISI from future symbols)
D(z): `post-cursor’ equalizer
(eliminates ISI from past symbols)
A(z )
Y (z )
C(z)
H(z)
W (z )
Postacademic Course on
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ˆ
A( z )
Module-3 Transmission
Lecture-5 Equalization
D(z)
Marc Moonen
K.U.Leuven-ESAT/SISTA
4/5/00
p. 29
30. Zero-forcing Equalizers
Decision Feedback equalization (DFE) :
- Problem : Error propagation
Decision errors at the output of the slicer cause a
corrupted estimate of the postcursor ISI.
Hence a single error causes a reduction of the noise
margin for a number of future decisions.
Results in increased bit-error rate.
A(z )
Y (z )
H(z)
W (z )
Postacademic Course on
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ˆ
A( z )
C(z)
Module-3 Transmission
Lecture-5 Equalization
D(z)
Marc Moonen
K.U.Leuven-ESAT/SISTA
4/5/00
p. 30
31. Zero-forcing Equalizers
`Figure of merit’
LE
DFE
MLSE
MF
• receiver with higher `figure of merit’ has lower error
probability
•
is `matched filter bound’ (transmission of 1 symbol)
• DFE-performance lower than MLSE-performance, as DFE
relies on only the first channel impulse response sample h0
(eliminating all other hi ‘s), while MLSE uses energy of all
taps hi . DFE benefits from minimum-phase property (cfr.
supra, p.20)
MF
Postacademic Course on
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Module-3 Transmission
Lecture-5 Equalization
Marc Moonen
K.U.Leuven-ESAT/SISTA
4/5/00
p. 31
32. MMSE Equalizers
• Zero-forcing equalizers: minimize noise at
slicer input under zero-ISI constraint
• Generalize the criterion of optimality to allow
for residual ISI at the slicer & reduce noise
variance at the slicer
=Minimum mean-square error equalizers
Postacademic Course on
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Module-3 Transmission
Lecture-5 Equalization
Marc Moonen
K.U.Leuven-ESAT/SISTA
4/5/00
p. 32
33. MMSE Equalizers
MMSE Linear Equalizer (LE) :
A(z )
ˆ
A( z )
Y (z )
C(z)
H(z)
W (z )
- combined minimization of ISI and noise leads to
1
)
*
z
* 1
S A ( z ).H ( z ).H ( * ) SW ( z )
z
S A ( z ).H * (
C ( z)
Postacademic Course on
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Module-3 Transmission
Lecture-5 Equalization
1
)
*
z
* 1
H ( z ).H ( * )
z
H *(
Marc Moonen
K.U.Leuven-ESAT/SISTA
2
n
4/5/00
p. 33
34. MMSE Equalizers
1
)
*
z
* 1
S A ( z ).H ( z ).H ( * ) SW ( z )
z
S A ( z ).H * (
C ( z)
-
1
)
*
z
* 1
H ( z ).H ( * )
z
H *(
2
W
S A (z ) 1
signal power spectrum (normalized)
2
SW ( z )
noise power spectrum (white)
W
1
for zero noise power -> zero-forcing C ( z ) H ( z )
* 1
H ( * ) (in the nominator) is a discrete-time matched filter,
z
often `difficult’ to realize in practice
(stable poles in H(z) introduce anticausal MF)
Postacademic Course on
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Module-3 Transmission
Lecture-5 Equalization
Marc Moonen
K.U.Leuven-ESAT/SISTA
4/5/00
p. 34
35. MMSE Equalizers
MMSE Decision Feedback Equalizer :
• MMSE-LE has correlated `slicer errors’
(=difference between slicer in- and output)
• MSE may be further reduced by incorporating a `whitening’
filter (prediction filter) E(z) for the slicer errors
A(z )
Y (z )
ˆ
A( z )
C(z)E(z)
H(z)
W (z )
1-E(z)
• E(z)=1 -> linear equalizer
• Theory & formulas : see textbooks
Postacademic Course on
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Module-3 Transmission
Lecture-5 Equalization
Marc Moonen
K.U.Leuven-ESAT/SISTA
4/5/00
p. 35
36. Fractionally Spaced Equalizers
Motivation:
• All equalizers (up till now) based on (whitened) matched
filter front-end, i.e. with symbol-rate sampling, preceded by
an (analog) front-end filter matched to the received pulse
p’(t)=p(t)*h(t).
• Symbol-rate sampling = below Nyquist-rate sampling
(aliasing!). Hence matched filter is crucial for performance !
• MF front-end requires analog filter, adapted to channel
h(t), hence difficult to realize...
• A fortiori: what if channel h(t) is unknown ?
• Synchronization problem : correct sampling phase is
crucial for performance !
Postacademic Course on
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Lecture-5 Equalization
Marc Moonen
K.U.Leuven-ESAT/SISTA
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p. 36
37. Fractionally Spaced Equalizers
• Fractionally spaced equalizers are based on Nyquist-rate
sampling, usually 2 x symbol-rate sampling (if excess
bandwidth < 100%).
• Nyquist-rate sampling also provides sufficient statistics,
hence provides appropriate front-end for optimal receivers.
• Sampler preceded by fixed (i.e. channel independent)
analog anti-aliasing (e.g. ideal low-pass) front-end filter.
• `Matched filter’ is moved to digital domain (after sampler).
• Avoids synchronization problem associated with MF
front-end.
Postacademic Course on
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Module-3 Transmission
Lecture-5 Equalization
Marc Moonen
K.U.Leuven-ESAT/SISTA
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p. 37
38. Fractionally Spaced Equalizers
• Input-output model for fractionally spaced equalization :
`symbol rate’ samples :
yk
~
... h0 .ak
~
h1.ak
1
~
h2 .ak
2
~
... wk
`intermediate’ samples :
yk
1/ 2
~
... h1/ 2 .ak
~
h3/ 2 .ak
1
~
h5 / 2 .ak
2
~
... wk
1/ 2
• may be viewed as 1-input/2-outputs system
Postacademic Course on
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Module-3 Transmission
Lecture-5 Equalization
Marc Moonen
K.U.Leuven-ESAT/SISTA
4/5/00
p. 38
39. Fractionally Spaced Equalizers
• Discrete-time matched filter + Equalizer (LE) :
1/2Ts
r (t )
F(f)
MF(z)
2
C(z)
ˆ
A( z )
equalizer
• Fractionally spaced equalizer (LE) :
1/2Ts
r (t )
F(f)
C(z)
2
ˆ
A( z )
Fractionally spaced equalizer
Postacademic Course on
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Module-3 Transmission
Lecture-5 Equalization
Marc Moonen
K.U.Leuven-ESAT/SISTA
4/5/00
p. 39
40. Fractionally Spaced Equalizers
• Fractionally spaced equalizer (DFE):
1/2Ts
r (t )
F(f)
C(z)
ˆ
A( z )
2
D(z)
• Theory & formulas : see textbooks & Lecture 6
Postacademic Course on
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Module-3 Transmission
Lecture-5 Equalization
Marc Moonen
K.U.Leuven-ESAT/SISTA
4/5/00
p. 40
41. Conclusions
• Cheaper alternatives to MLSE, based on
equalization filters + memoryless decision
device (slicer)
• Symbol-rate equalizers :
-LE versus DFE
-zero-forcing versus MMSE
-optimal with matched filter front-end, but several
assumptions underlying this structure are often
violated in practice
• Fractionally spaced equalizers (see also Lecture-6)
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Lecture-5 Equalization
Marc Moonen
K.U.Leuven-ESAT/SISTA
4/5/00
p. 41
42. Assignment 3.1
• Symbol-rate zero-forcing linear equalizer has
H 1 ( z)
C ( z)
i.e. a finite impulse response (`all-zeroes’) filter
H ( z)
h0
h1.z
1
h2 .z
2
is turned into an infinite impulse response filter
C ( z ) 1 /(h0
1
h1.z
h2 .z 2 )
• Investigate this statement for the case of fractionally spaced
equalization, for a simple channel model
yk
yk
h0 .ak
1/ 2
h1.ak
h1/ 2 .ak
1
h2 .ak
h3 / 2 .ak
1
2
h5 / 2 .ak
2
and discover that there exist finite-impulse response inverses in this
case. This represents a significant advantage in practice. Investigate
the minimal filter length for the zero-forcing equalization filter.
Postacademic Course on
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Module-3 Transmission
Lecture-5 Equalization
Marc Moonen
K.U.Leuven-ESAT/SISTA
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p. 42