This document provides an overview of circuits and communication topics covered in an electrical engineering course. It discusses voltage sources, driving circuits, operational amplifier circuits, and communications concepts like matched filtering and receiver synchronization. The goal is to introduce practical circuit ideas and fundamental communication principles, with a focus on robustly detecting signals and data in the presence of noise. Worked examples are provided for repeating codes, on-off keying, and antipodal signalling transmission scenarios.
This document provides an introduction to the discrete Fourier transform (DFT) from David S. Gilliam of the Department of Mathematics at Texas Tech University. It defines the DFT and inverse DFT, and discusses their relationship to the continuous Fourier transform and Fourier series. The DFT is presented as approximating the continuous Fourier transform by sampling an analog signal at discrete time intervals. Matlab code is provided as an example to compute the DFT and compare it to the exact Fourier transform of a sample function.
Paper, presented at the Workshop “Music, Mind, Invention”, 30.-31.March 2012, Ewing, NJ.
When a 2D Fourier Transform is applied to piano roll plots which are often used in sequencer software, the resulting 2D graphic is a novel music visualization which reveals internal musical structure. This visualization converts the set of musical notes from the notation display in the piano roll plot to a display which shows structure over time and spectrum within a set musical time period. The transformation is reversible, which means that it also can be used as a novel interface for editing music. The concept of this visualization is demonstrated by software which was written for using MIDI files and creating the visualization with the Fast Fourier Transform (FFT) algorithm. This software demonstrates the live real-time display of this visualization in replay of MIDI files or by music input through a connected MIDI keyboard. The resulting display is independent of pitch transformation or tempo. This visualization approach can be used for musicology studies, for music fingerprinting, comparing composition styles, and for a new creative composition method.
fourier representation of signal and systemsSugeng Widodo
This document provides an overview of Fourier analysis concepts including:
- The Fourier transform decomposes a signal into its constituent frequencies.
- Properties of the Fourier transform like linearity, time/frequency shifting, and modulation are discussed.
- The Fourier transform of a time derivative or integral is related to the original Fourier transform.
- Convolution and correlation theorems explain how time domain operations translate to the frequency domain.
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.
This document reviews the Fourier transform and its properties. It defines the Fourier transform and inverse Fourier transform. The Fourier transform of a signal decomposes it into its frequency components. Properties covered include linearity, time/frequency shifting, modulation, convolution, and more. Examples of Fourier transforms are given for rectangular pulses and Dirac delta functions. Applications to signals like DC, complex exponentials, and sinusoids are described. Proofs can be found in the referenced textbook.
DSP_2018_FOEHU - Lec 06 - FIR Filter DesignAmr E. Mohamed
This lecture discusses the design of finite impulse response (FIR) filters. It introduces the window method for FIR filter design, which involves truncating the ideal impulse response with a window function to obtain a causal FIR filter. Common window functions are presented such as rectangular, triangular, Hanning, Hamming, and Blackman windows. These windows trade off main lobe width and side lobe levels. The document provides an example design of a low-pass FIR filter using the Hamming window to meet given passband and stopband specifications.
This document provides an overview of circuits and communication topics covered in an electrical engineering course. It discusses voltage sources, driving circuits, operational amplifier circuits, and communications concepts like matched filtering and receiver synchronization. The goal is to introduce practical circuit ideas and fundamental communication principles, with a focus on robustly detecting signals and data in the presence of noise. Worked examples are provided for repeating codes, on-off keying, and antipodal signalling transmission scenarios.
This document provides an introduction to the discrete Fourier transform (DFT) from David S. Gilliam of the Department of Mathematics at Texas Tech University. It defines the DFT and inverse DFT, and discusses their relationship to the continuous Fourier transform and Fourier series. The DFT is presented as approximating the continuous Fourier transform by sampling an analog signal at discrete time intervals. Matlab code is provided as an example to compute the DFT and compare it to the exact Fourier transform of a sample function.
Paper, presented at the Workshop “Music, Mind, Invention”, 30.-31.March 2012, Ewing, NJ.
When a 2D Fourier Transform is applied to piano roll plots which are often used in sequencer software, the resulting 2D graphic is a novel music visualization which reveals internal musical structure. This visualization converts the set of musical notes from the notation display in the piano roll plot to a display which shows structure over time and spectrum within a set musical time period. The transformation is reversible, which means that it also can be used as a novel interface for editing music. The concept of this visualization is demonstrated by software which was written for using MIDI files and creating the visualization with the Fast Fourier Transform (FFT) algorithm. This software demonstrates the live real-time display of this visualization in replay of MIDI files or by music input through a connected MIDI keyboard. The resulting display is independent of pitch transformation or tempo. This visualization approach can be used for musicology studies, for music fingerprinting, comparing composition styles, and for a new creative composition method.
fourier representation of signal and systemsSugeng Widodo
This document provides an overview of Fourier analysis concepts including:
- The Fourier transform decomposes a signal into its constituent frequencies.
- Properties of the Fourier transform like linearity, time/frequency shifting, and modulation are discussed.
- The Fourier transform of a time derivative or integral is related to the original Fourier transform.
- Convolution and correlation theorems explain how time domain operations translate to the frequency domain.
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.
This document reviews the Fourier transform and its properties. It defines the Fourier transform and inverse Fourier transform. The Fourier transform of a signal decomposes it into its frequency components. Properties covered include linearity, time/frequency shifting, modulation, convolution, and more. Examples of Fourier transforms are given for rectangular pulses and Dirac delta functions. Applications to signals like DC, complex exponentials, and sinusoids are described. Proofs can be found in the referenced textbook.
DSP_2018_FOEHU - Lec 06 - FIR Filter DesignAmr E. Mohamed
This lecture discusses the design of finite impulse response (FIR) filters. It introduces the window method for FIR filter design, which involves truncating the ideal impulse response with a window function to obtain a causal FIR filter. Common window functions are presented such as rectangular, triangular, Hanning, Hamming, and Blackman windows. These windows trade off main lobe width and side lobe levels. The document provides an example design of a low-pass FIR filter using the Hamming window to meet given passband and stopband specifications.
This document describes an audio compression system using discrete wavelet transform and a psychoacoustic model. The system analyzes audio signals using wavelet decomposition, applies a psychoacoustic model to estimate masking thresholds, quantizes coefficients below the thresholds, and encodes the results. Evaluation showed the system achieved over 50% bit rate reduction with transparent quality on music signals like violin, drums, piano and vocals based on subjective listening tests.
Dsp 2018 foehu - lec 10 - multi-rate digital signal processingAmr E. Mohamed
This document discusses multi-rate digital signal processing and concepts related to sampling continuous-time signals. It begins by introducing discrete-time processing of continuous signals using an ideal continuous-to-discrete converter. It then covers the Nyquist sampling theorem and relationships between continuous and discrete Fourier transforms. It discusses ideal and practical reconstruction using zero-order hold and anti-imaging filters. Finally, it introduces the concepts of downsampling and upsampling in multi-rate digital signal processing systems.
The document analyzes a method for comparing two audio files to detect human errors using fast Fourier transforms (FFT). It describes using FFT to convert audio files from the time domain to the frequency domain. It then calculates the mean squared error (MSE) between the normalized spectral densities of the two files. A low MSE would indicate the files are identical, while a higher MSE shows a difference. The document provides the steps and flowchart used, and includes examples of Matlab and Labview code implementing the comparison method on identical and non-identical audio files.
This document provides an overview of how linear systems analysis and Fourier transforms can be applied to analyze 2-dimensional optical images and optical systems. It explains that plane waves serve as the eigenfunctions for linear shift invariant optical systems, just as complex exponentials serve as the eigenfunctions for linear time invariant electrical systems. The Fourier transform can be used to decompose an optical image into its plane wave spectrum, and optical systems can be analyzed by multiplying the image spectrum by the system's optical transfer function and taking the inverse Fourier transform. As an example, it describes how a thin lens can be modeled as a phase shifting device and its optical transfer function calculated.
Design and Implementation of Low Ripple Low Power Digital Phase-Locked LoopCSCJournals
We propose a phase-locked loop (PLL) architecture, which reduces the double frequency ripple without increasing the order of loop filter. Proposed architecture uses quadrature numerically–controlled oscillator (NCO) to provide two output signals with phase difference of π/2. One of them is subtracted from the input signal before multiplying with the other output of NCO. The system also provides stability in case the input signal has noise in amplitude or phase. The proposed structure is implemented using field programmable gate array (FPGA), which dissipates 15.44mw and works at clock frequency of 155.8 MHz.
This document discusses pulse modulation techniques in communications. It begins by reviewing continuous-wave modulation techniques studied previously, such as amplitude modulation and angle modulation. It then previews that pulse modulation will be studied next, including analog pulse modulation where a pulse feature varies continuously with the message, and digital pulse modulation using a sequence of coded pulses. The document provides explanations and equations regarding sampling of continuous-time signals, the sampling theorem, and recovery of the original analog signal from its samples. It also introduces pulse amplitude modulation (PAM) using natural and flat-top sampling, as well as pulse duration modulation (PDM) and pulse position modulation (PPM).
The document discusses Fast Fourier Transform (FFT) analysis. It begins by explaining what Fourier Transform and Discrete Fourier Transform (DFT) are and how they convert signals from the time domain to the frequency domain. It then states that FFT is an efficient algorithm for performing DFT, allowing it to be done much faster on computers. The document proceeds to describe different types of FFT algorithms like Cooley-Tukey, Prime Factor, Bruun's, and Rader's algorithms. It concludes by discussing characteristics of FFT like approximation, accuracy, and complexity bounds, as well as applications and how FFT can be used to analyze vibration signals in the frequency domain.
The receiver structure consists of four main components:
1. A matched filter that maximizes the SNR by matching the source impulse and channel.
2. An equalizer that removes intersymbol interference.
3. A timing component that determines the optimal sampling time using an eye diagram.
4. A decision component that determines whether the received bit is a 0 or 1 based on a threshold.
The performance of the receiver depends on factors like noise, equalization technique used, and timing accuracy. The bit error rate can be estimated using tools like error functions.
This document discusses principles of communication and representation of signals. It begins with an introduction to the communication process and challenges involved. Signals exist in the time and frequency domains, and Fourier analysis using the Fourier series and Fourier transform helps characterize signals in the frequency domain. Periodic signals can be represented by a Fourier series which decomposes the signal into a sum of complex exponentials at discrete frequencies that are integer multiples of the fundamental frequency. Examples are provided to illustrate calculation of Fourier coefficients and representation of periodic signals in the exponential and trigonometric forms of the Fourier series. Spectral plots from a spectrum analyzer are also presented for various waveforms.
The document discusses genetic motifs and promoters. It explains that transcription factor binding sites (TFBS) are short DNA sequences that transcription factors bind to in order to regulate gene expression. It then describes how the assembly of promoter protein complexes occurs through multiple stages involving different transcription factors binding to TFBS. The document also introduces information theory concepts like entropy and mutual information that can be used to detect motifs through measuring correlations between sequences. It provides an example algorithm that uses a sliding window approach to calculate mutual information between a probe TFBS sequence and candidate sequences in order to identify new potential TFBSs.
Nyquist criterion for distortion less baseband binary channelPriyangaKR1
binary transmission system
From design point of view – frequency response of the channel and transmitted pulse shape are specified; the frequency response of the transmit and receive filters has to be determined so as to reconstruct [bk]
1) Randomly select positions to project sequences onto lower-dimensional "buckets" based on letters at those positions.
2) Recover motifs from buckets containing multiple sequences by building frequency matrices and refining with EM.
3) The best motif is the one with the highest score, where score is based on the likelihood ratio of sequences matching the motif model versus background.
Noise reduction is the process of removing noise from a signal. In this project, two audio files are given: (1) speech.au and (2) noisy_speech.au. The first file contains the original speech signal and the second one contains the noisy version of the first signal. The objective of this project is to reduce the noise from the noisy file
Echo and reverberation effects are used extensively in the music industry. Here we will design a digital filter that will create the echo and reverb effect on audio signals.
fast-Fourier-transform-presentation and Fourier transform for wave
in
signal possessing for
physics and
geophysics
spectra analysis
periodic and non periodic wave
data sampling
The Nyquist frequency
1. The team verified the relationship between music and math by measuring the frequencies of notes played on an instrument.
2. Their results supported the hypotheses that the frequency of each octave is twice the previous octave, the logarithmic distance between notes is constant, and simpler frequency ratios produce more harmonious intervals.
3. Potential improvements included conducting the experiment in a quiet room and maintaining a fixed distance between the microphone and instrument.
Ch6 digital transmission of analog signal pg 99Prateek Omer
This document discusses digital transmission of analog signals using techniques like Pulse Code Modulation (PCM), Differential Pulse Code Modulation (DPCM), and Delta Modulation (DM).
It begins by introducing the benefits of digital transmission over analog transmission, such as regeneration of signals to eliminate distortion and noise, easy storage and forwarding of messages, and multiplexing of signals.
It then describes the basic operations in PCM - time discretization through sampling and amplitude discretization through quantization. A PCM system samples an analog signal, quantizes the samples, encodes the quantized values into binary code words, transmits the code words digitally, decodes and reconstructs the analog signal from the samples.
This document discusses correlative-level coding and its applications in baseband pulse transmission systems. Correlative-level coding introduces controlled intersymbol interference to increase signaling rate. It allows partial response signaling and maximum likelihood detection at the receiver. Specific techniques discussed include duobinary signaling and modified duobinary signaling. The document also covers tapped-delay line equalization using adaptive algorithms like least mean square to compensate for channel distortion. Decision feedback equalization and its implementation are summarized as well. Eye patterns are described as a tool to evaluate signal quality in such systems.
MRI uses magnetic fields and radio waves to generate images of the inside of the body. It works by aligning hydrogen atoms in the body and recording their signals as the atoms relax. Three key steps in MRI image formation are slice selection, frequency encoding, and phase encoding. Slice selection uses magnetic field gradients to excite only protons in a thin slice. Frequency encoding assigns spatial positions to signal frequencies. Phase encoding adds location-dependent phase shifts. Together these steps encode spatial information into the measured MR signal, allowing reconstruction of 2D or 3D images. The MR signal is represented mathematically in k-space, which is sampled during the encoding and readout process to generate the final image in image space.
Speech signal time frequency representationNikolay Karpov
This lecture discusses spectrogram analysis and the short-term discrete Fourier transform. It defines normalized time and frequency, examines the effect of window length on time-frequency resolution, and derives descriptions of frequency and time resolution. It also reviews properties of the discrete Fourier transform and illustrates the uncertainty principle with examples.
This document provides an overview of discrete-time signals and systems in digital signal processing (DSP). It discusses key concepts such as:
1) Discrete-time signals which are represented by sequences of numbers and how common signals like impulses and steps are represented.
2) Discrete-time systems which take a discrete-time signal as input and produce an output signal through a mathematical algorithm, with the impulse response characterizing the system.
3) Important properties of linear time-invariant (LTI) systems including superposition, time-shifting of inputs and outputs, and representation using convolution sums or difference equations.
This document discusses the design of finite impulse response (FIR) filters. It begins by describing the basic FIR filter model and properties such as filter order and length. It then covers topics such as linear phase response, different filter types (low-pass, high-pass, etc.), deriving the ideal impulse response, and filter specification in terms of passband/stopband edges and ripple levels. The document concludes by outlining the common FIR design method of windowing the ideal impulse response, describing popular window functions, and providing a step-by-step example of designing a low-pass FIR filter using the Hamming window.
This document describes an audio compression system using discrete wavelet transform and a psychoacoustic model. The system analyzes audio signals using wavelet decomposition, applies a psychoacoustic model to estimate masking thresholds, quantizes coefficients below the thresholds, and encodes the results. Evaluation showed the system achieved over 50% bit rate reduction with transparent quality on music signals like violin, drums, piano and vocals based on subjective listening tests.
Dsp 2018 foehu - lec 10 - multi-rate digital signal processingAmr E. Mohamed
This document discusses multi-rate digital signal processing and concepts related to sampling continuous-time signals. It begins by introducing discrete-time processing of continuous signals using an ideal continuous-to-discrete converter. It then covers the Nyquist sampling theorem and relationships between continuous and discrete Fourier transforms. It discusses ideal and practical reconstruction using zero-order hold and anti-imaging filters. Finally, it introduces the concepts of downsampling and upsampling in multi-rate digital signal processing systems.
The document analyzes a method for comparing two audio files to detect human errors using fast Fourier transforms (FFT). It describes using FFT to convert audio files from the time domain to the frequency domain. It then calculates the mean squared error (MSE) between the normalized spectral densities of the two files. A low MSE would indicate the files are identical, while a higher MSE shows a difference. The document provides the steps and flowchart used, and includes examples of Matlab and Labview code implementing the comparison method on identical and non-identical audio files.
This document provides an overview of how linear systems analysis and Fourier transforms can be applied to analyze 2-dimensional optical images and optical systems. It explains that plane waves serve as the eigenfunctions for linear shift invariant optical systems, just as complex exponentials serve as the eigenfunctions for linear time invariant electrical systems. The Fourier transform can be used to decompose an optical image into its plane wave spectrum, and optical systems can be analyzed by multiplying the image spectrum by the system's optical transfer function and taking the inverse Fourier transform. As an example, it describes how a thin lens can be modeled as a phase shifting device and its optical transfer function calculated.
Design and Implementation of Low Ripple Low Power Digital Phase-Locked LoopCSCJournals
We propose a phase-locked loop (PLL) architecture, which reduces the double frequency ripple without increasing the order of loop filter. Proposed architecture uses quadrature numerically–controlled oscillator (NCO) to provide two output signals with phase difference of π/2. One of them is subtracted from the input signal before multiplying with the other output of NCO. The system also provides stability in case the input signal has noise in amplitude or phase. The proposed structure is implemented using field programmable gate array (FPGA), which dissipates 15.44mw and works at clock frequency of 155.8 MHz.
This document discusses pulse modulation techniques in communications. It begins by reviewing continuous-wave modulation techniques studied previously, such as amplitude modulation and angle modulation. It then previews that pulse modulation will be studied next, including analog pulse modulation where a pulse feature varies continuously with the message, and digital pulse modulation using a sequence of coded pulses. The document provides explanations and equations regarding sampling of continuous-time signals, the sampling theorem, and recovery of the original analog signal from its samples. It also introduces pulse amplitude modulation (PAM) using natural and flat-top sampling, as well as pulse duration modulation (PDM) and pulse position modulation (PPM).
The document discusses Fast Fourier Transform (FFT) analysis. It begins by explaining what Fourier Transform and Discrete Fourier Transform (DFT) are and how they convert signals from the time domain to the frequency domain. It then states that FFT is an efficient algorithm for performing DFT, allowing it to be done much faster on computers. The document proceeds to describe different types of FFT algorithms like Cooley-Tukey, Prime Factor, Bruun's, and Rader's algorithms. It concludes by discussing characteristics of FFT like approximation, accuracy, and complexity bounds, as well as applications and how FFT can be used to analyze vibration signals in the frequency domain.
The receiver structure consists of four main components:
1. A matched filter that maximizes the SNR by matching the source impulse and channel.
2. An equalizer that removes intersymbol interference.
3. A timing component that determines the optimal sampling time using an eye diagram.
4. A decision component that determines whether the received bit is a 0 or 1 based on a threshold.
The performance of the receiver depends on factors like noise, equalization technique used, and timing accuracy. The bit error rate can be estimated using tools like error functions.
This document discusses principles of communication and representation of signals. It begins with an introduction to the communication process and challenges involved. Signals exist in the time and frequency domains, and Fourier analysis using the Fourier series and Fourier transform helps characterize signals in the frequency domain. Periodic signals can be represented by a Fourier series which decomposes the signal into a sum of complex exponentials at discrete frequencies that are integer multiples of the fundamental frequency. Examples are provided to illustrate calculation of Fourier coefficients and representation of periodic signals in the exponential and trigonometric forms of the Fourier series. Spectral plots from a spectrum analyzer are also presented for various waveforms.
The document discusses genetic motifs and promoters. It explains that transcription factor binding sites (TFBS) are short DNA sequences that transcription factors bind to in order to regulate gene expression. It then describes how the assembly of promoter protein complexes occurs through multiple stages involving different transcription factors binding to TFBS. The document also introduces information theory concepts like entropy and mutual information that can be used to detect motifs through measuring correlations between sequences. It provides an example algorithm that uses a sliding window approach to calculate mutual information between a probe TFBS sequence and candidate sequences in order to identify new potential TFBSs.
Nyquist criterion for distortion less baseband binary channelPriyangaKR1
binary transmission system
From design point of view – frequency response of the channel and transmitted pulse shape are specified; the frequency response of the transmit and receive filters has to be determined so as to reconstruct [bk]
1) Randomly select positions to project sequences onto lower-dimensional "buckets" based on letters at those positions.
2) Recover motifs from buckets containing multiple sequences by building frequency matrices and refining with EM.
3) The best motif is the one with the highest score, where score is based on the likelihood ratio of sequences matching the motif model versus background.
Noise reduction is the process of removing noise from a signal. In this project, two audio files are given: (1) speech.au and (2) noisy_speech.au. The first file contains the original speech signal and the second one contains the noisy version of the first signal. The objective of this project is to reduce the noise from the noisy file
Echo and reverberation effects are used extensively in the music industry. Here we will design a digital filter that will create the echo and reverb effect on audio signals.
fast-Fourier-transform-presentation and Fourier transform for wave
in
signal possessing for
physics and
geophysics
spectra analysis
periodic and non periodic wave
data sampling
The Nyquist frequency
1. The team verified the relationship between music and math by measuring the frequencies of notes played on an instrument.
2. Their results supported the hypotheses that the frequency of each octave is twice the previous octave, the logarithmic distance between notes is constant, and simpler frequency ratios produce more harmonious intervals.
3. Potential improvements included conducting the experiment in a quiet room and maintaining a fixed distance between the microphone and instrument.
Ch6 digital transmission of analog signal pg 99Prateek Omer
This document discusses digital transmission of analog signals using techniques like Pulse Code Modulation (PCM), Differential Pulse Code Modulation (DPCM), and Delta Modulation (DM).
It begins by introducing the benefits of digital transmission over analog transmission, such as regeneration of signals to eliminate distortion and noise, easy storage and forwarding of messages, and multiplexing of signals.
It then describes the basic operations in PCM - time discretization through sampling and amplitude discretization through quantization. A PCM system samples an analog signal, quantizes the samples, encodes the quantized values into binary code words, transmits the code words digitally, decodes and reconstructs the analog signal from the samples.
This document discusses correlative-level coding and its applications in baseband pulse transmission systems. Correlative-level coding introduces controlled intersymbol interference to increase signaling rate. It allows partial response signaling and maximum likelihood detection at the receiver. Specific techniques discussed include duobinary signaling and modified duobinary signaling. The document also covers tapped-delay line equalization using adaptive algorithms like least mean square to compensate for channel distortion. Decision feedback equalization and its implementation are summarized as well. Eye patterns are described as a tool to evaluate signal quality in such systems.
MRI uses magnetic fields and radio waves to generate images of the inside of the body. It works by aligning hydrogen atoms in the body and recording their signals as the atoms relax. Three key steps in MRI image formation are slice selection, frequency encoding, and phase encoding. Slice selection uses magnetic field gradients to excite only protons in a thin slice. Frequency encoding assigns spatial positions to signal frequencies. Phase encoding adds location-dependent phase shifts. Together these steps encode spatial information into the measured MR signal, allowing reconstruction of 2D or 3D images. The MR signal is represented mathematically in k-space, which is sampled during the encoding and readout process to generate the final image in image space.
Speech signal time frequency representationNikolay Karpov
This lecture discusses spectrogram analysis and the short-term discrete Fourier transform. It defines normalized time and frequency, examines the effect of window length on time-frequency resolution, and derives descriptions of frequency and time resolution. It also reviews properties of the discrete Fourier transform and illustrates the uncertainty principle with examples.
This document provides an overview of discrete-time signals and systems in digital signal processing (DSP). It discusses key concepts such as:
1) Discrete-time signals which are represented by sequences of numbers and how common signals like impulses and steps are represented.
2) Discrete-time systems which take a discrete-time signal as input and produce an output signal through a mathematical algorithm, with the impulse response characterizing the system.
3) Important properties of linear time-invariant (LTI) systems including superposition, time-shifting of inputs and outputs, and representation using convolution sums or difference equations.
This document discusses the design of finite impulse response (FIR) filters. It begins by describing the basic FIR filter model and properties such as filter order and length. It then covers topics such as linear phase response, different filter types (low-pass, high-pass, etc.), deriving the ideal impulse response, and filter specification in terms of passband/stopband edges and ripple levels. The document concludes by outlining the common FIR design method of windowing the ideal impulse response, describing popular window functions, and providing a step-by-step example of designing a low-pass FIR filter using the Hamming window.
The document discusses Fourier analysis techniques. It covers topics like line spectra and Fourier series, including periodic signals and average power. Key aspects covered include phasor representation of sinusoids, convergence conditions of Fourier series, and Parseval's power theorem relating signal power to Fourier coefficients.
This document discusses power spectral density (PSD) and linear time-invariant (LTI) systems. It covers the following key points:
1. The PSD of a wide-sense stationary (WSS) random process is the Fourier transform of its autocorrelation function and represents the average power density over frequency.
2. When a random signal passes through an LTI system, the output is also a random process. The input-output relations between spectral densities and correlation functions are described.
3. Optimal linear minimum mean square error (MMSE) estimation of a random signal involves designing a filter to minimize the error between the estimated and true signals based on an observation.
EXPERT SYSTEMS AND SOLUTIONS
Project Center For Research in Power Electronics and Power Systems
IEEE 2010 , IEEE 2011 BASED PROJECTS FOR FINAL YEAR STUDENTS OF B.E
Email: expertsyssol@gmail.com,
Cell: +919952749533, +918608603634
www.researchprojects.info
OMR, CHENNAI
IEEE based Projects For
Final year students of B.E in
EEE, ECE, EIE,CSE
M.E (Power Systems)
M.E (Applied Electronics)
M.E (Power Electronics)
Ph.D Electrical and Electronics.
Training
Students can assemble their hardware in our Research labs. Experts will be guiding the projects.
EXPERT GUIDANCE IN POWER SYSTEMS POWER ELECTRONICS
We provide guidance and codes for the for the following power systems areas.
1. Deregulated Systems,
2. Wind power Generation and Grid connection
3. Unit commitment
4. Economic Dispatch using AI methods
5. Voltage stability
6. FLC Control
7. Transformer Fault Identifications
8. SCADA - Power system Automation
we provide guidance and codes for the for the following power Electronics areas.
1. Three phase inverter and converters
2. Buck Boost Converter
3. Matrix Converter
4. Inverter and converter topologies
5. Fuzzy based control of Electric Drives.
6. Optimal design of Electrical Machines
7. BLDC and SR motor Drives
This document discusses signals and their representations. It covers:
1. Continuous-time signals which are defined for every instant in time and discrete-time signals which are defined at particular time intervals.
2. Representations of signals including graphical, tabular, functional, and sequence representations.
3. Elementary signals including unit step, unit impulse, and unit ramp signals for both continuous and discrete time. The relationships between these signals are also described.
This document discusses wideband frequency modulation (FM) and its properties. It begins by introducing the concept of FM and defining terms like modulation index and frequency deviation. It then shows that the FM signal can be expressed as a complex Fourier series involving Bessel functions. The spectrum of the FM signal is derived and shown to consist of sidebands spaced at multiples of the modulating frequency away from the carrier frequency. For small modulation indices, the spectrum reduces to the carrier and first sidebands, corresponding to narrowband FM.
Classifications of signals vi sem cse it6502rohinisubburaj
This document provides an introduction to signals and their classification. It discusses continuous-time signals, discrete-time signals, periodic signals, non-periodic signals, even and odd signals, and signal energy and power. Continuous-time signals have a value for all points in time, while discrete-time signals have values for specific points in time formed by sampling. Signals can be classified as deterministic or non-deterministic, periodic or non-periodic, even or odd. The document also covers operations on signals like time shifting and scaling, and defines energy and power for discrete-time signals. Textbooks and references on digital signal processing are listed.
The document summarizes Lecture 7 which covered:
1) A review of Lecture 6 on PCM waveforms and the remaining portion of Chapter 2 on spectral densities of PCM waveforms and multi-level signaling.
2) An overview of Chapter 3 on baseband demodulation/detection including matched filters, correlators, Bayes' decision criterion, and maximum likelihood detection.
3) Key aspects of line codes including how pulse shaping can control the signal spectrum and ensure symbol transitions, comparisons of line codes based on power spectral density, DC component, and bandwidth.
DSP_2018_FOEHU - Lec 08 - The Discrete Fourier TransformAmr E. Mohamed
The document provides an overview of the Discrete Fourier Transform (DFT). It begins by discussing limitations of the discrete-time Fourier transform (DTFT) and z-transform in that they are defined for infinite sequences and continuous variables. The DFT avoids these issues by being a numerically computable transform for finite discrete-time signals. It works by taking a finite signal, making it periodic, and computing its discrete Fourier transform which is a discrete frequency spectrum. This makes the DFT highly suitable for digital signal processing. The document then provides details on computation of the DFT and its relationship to the DTFT and z-transform.
Slide set presented for the Wireless Communication module at Jacobs University Bremen, Fall 2015.
Teacher: Dr. Stefano Severi, assistant: Andrei Stoica
This document discusses signals and systems. It defines signals as physical quantities that vary with respect to time, space, or another independent variable. Signals can be classified as discrete time or continuous time. It also defines unit impulse and unit step functions for discrete and continuous time. Periodic and aperiodic signals are discussed. The Fourier series and Fourier transform are introduced as ways to represent signals in the frequency domain. The Laplace transform, which generalizes the Fourier transform, is also mentioned. Key properties of linear time-invariant systems like superposition, time-invariance, and convolution are covered. Finally, sampling theory and the z-transform, which is analogous to the Laplace transform for discrete-time systems, are summarized at a high level
This document provides an introduction to the Discrete Fourier Transform (DFT) including its definition, relationship to the continuous Fourier transform and Fourier series, and examples of its computation and applications. Specifically:
- The DFT takes a periodic discrete-time signal and transforms it to its frequency spectrum. It is defined by a summation formula that relates the original and transformed sequences.
- The DFT is related to the continuous Fourier transform as an approximation using discrete sampling. It is also related to the Fourier series representation of periodic functions.
- Examples are provided to demonstrate computing the DFT using matrix multiplication and the fast Fourier transform (FFT) algorithm in Matlab. Applications to spectral analysis and filtering are discussed.
Similar to Extracting Tones of Gamelan with STFT (16)
1. Extracting Tones of
Gamelan Musical Instrument “Saron of Balungan”
with Short Time Fourier Transform Method
Arief Mubarok, Eric Jansen, Hendra Tri Sadewa
arief.mubarok10@mhs.ee.its.ac.id, eric10@mhs.ee.its.ac.id, hendra.tri.sadewa10@mhs.ee.its.ac.id
Adviser:
Dr. Ir. Yoyon Kusnendar Suprapto, M.Sc
yoyonsuprapto@ee.its.ac.id
July 7, 2011
Abstract
Gamelan is a musical ensemble from Indonesia. In General, gamelan is made from bronze and brass. Today,
gamelan music is fairly seen in normal occasions. Gamelan orchestra is only held in special events. e.g.
puppet show or wayang kulit. Due to highly expensive the instrument costs and the influences of modern
music, role of gamelan as one of Indonesian characteristic music is getting less enthusiasts. In contrast to main
role of gamelan in Indonesia, the amount of foreigners in dedicating to gamelan is increasing extensively and
indicating great enthusiasm.
This research refers to determine tones of balungan(1) musical instrument, particularly in saron using Short
Time Fourier Transform or STFT, in purpose to analyze signals in frequency and time domains.
1 Preface lan, e.g. slicing frequency constraints. Gamelan has
several instruments, that in each instrument has its
The saron typically consists of seven bronze bars on own typical tone. This research refers to specific
top of a resonating frame (rancak) and plays melody gamelan: saron of balungan(1) . saron of balungan(1) has
along with slenthem(2) . It is usually about 20 cm (8in) five tones: ji, ro, lu, ma and nem. In each tone has
high, and is played on the floor by a seated performer. its own frequency. The range of notes is defined in
In slendro(3) scale, the bars are 6-1-2-3-5-6-1; This can following table 1.
vary from gamelan to gamelan, or even among instru-
ments in the same gamelan. Slendro(3) instruments Tones Range of Frequencies
commonly have only six keys. It provides the core Ji 504 - 539 Hz
melody (balungan(1) ) in the gamelan orchestra. Sarons Ro 574 - 610 Hz
typically come in a number often sizes, from smallest Lu 688 - 703 Hz
to largest: saron panerus (also: peking), saron barung Ma 792 - 799 Hz
(sometimes just saron) and saron demung (often just Nem 909 - 926 Hz
called demung). Each one of those is pitched an oc-
tave below the previous. The slenthem(2) or slentho
Table 1. Range of Frequencies in Gamelan Slendro(3)
performs a similar function to the sarons one octave
below the demung.
Defining tones according to frequency, Short Time Any interventions from other balungan instruments,
Fourier Transform (STFT) renders output in form of e.g. demung and bonang are disaggregated, as result-
filtered sound based on window. STFT is developed ing saron tones.
from Fast Fourier Transform (FFT). The algorithm of
(1) The balungan (Javanese: skeleton, frame) is sometimes called the “core
STFT captures input signals in t time, then the results melody” of a Javanese gamelan composition. This corresponds to the view
are generated in time and frequency domains. that gamelan music is heterophonic: the balungan is then the melody which
is being elaborated.
Basicly, STFT has the same definition to Fourier (2) Slenthem frequently plays the same basic melody as that of the saron.
Transform. The difference between the both is in win- Occasionally, it does have its own important part to play. It is low in pitch,
and its sound sustains for a relatively long period of time because of the
dow function. With window function, STFT renders or tubular resonators below each bar.
slices signals from time domain to frequency domain. (3) Slendroof the two salendro by the Sundanese is aused in Indonesian
scale, one
or called
most common scales (laras)
pentatonic
window function aims at recognizing notes in game- gamelan music, the other being p´log. e
1
2. 2 Theoritical Methods 2.2 Discrete Fourier Transform
In general, Discrete Fourier Transform or DFT is similar
Analyzing notes in form of signals, is described in
to native fourier transform. In distinct manner, DFT
following figure 1.
needs input function as discrete signal. Theoritically,
DFT is defined as following:
Input notations signal n−1
Xk = x[n]ωkn , k = 0,1,2,...,N-1
n (5)
n=0
N−1
X(ωk ) x(tn )e− jωk tn , k = 0,1,2,...,N-1 (6)
Signals rendered into time
n=0
and/or frequency domains
where ’ ’ means “is defined as” or “equals by defini-
tion”, and
N−1
Define frequency
fundamental f (n) f (0) + f (1) + ... + f (N − 1)
n=0
x(tn ) input signal amplitude (real and complex)
at time tn
Analyze frequency of
tn nT = nth sampling instant (sec), n an
tones that rendered
integer ≥ 0
T sampling interval (sec)
X(ωk ) spectrum of x, at frequency ωk
Determine occuring
notes in time domain ωk kΩ = kth frequency sample (radians per
second)
figure 1. Signal Processing System 2π
Ω = radian-frequency sampling interval
NT
(rad/sec)
2.1 Fast Fourier Transform
fs 1/T = sampling rate (Hz)
The term Fast Fourier Transform or FFT refers to an effi- N = number of time samples (integer).
cient implementation of the Discrete Fourier Transform
(DFT). FFT is commonly used in analyzing signal,
e.g. filtering, analyzing correlation and spectrum. 2.3 Short Time Fourier Transform
Fast Fourier Transform is developed from DFT or Dis- Short Time Fourier Transform or STFT or short-term
crete Fourier Transform. Mainly used in transforming Fourier Transform is a powerful general-purpose tool
signal from time domain to frequency domain. The for audio signal processing. It defines a partic-
method is intended to process signals in spectral sub- ularly useful class of time-frequency distributions
straction. Fast Fourier Transform or FFT is defined as which specify complex amplitude versus time and
following: frequency for any signal. Tuning the STFT parame-
ters for the following applications:
H= h(t)e− jωt dt (1) 1. Approximating the time-frequency analysis per-
f formed by the ear for purposes of spectral display.
whereas ω = 2π = 2π f T (2)
fs 2. Measuring model parameters in a short-time spec-
trum.
As transformed into discrete is defined as following:
The definition of the continuous-time STFT is:
N−1 ∞
H(kω0 ) = h(nT)e− jkω0 nT (3) STFTx(t) = X(τ, ω) = x(t)w(t − τ)e− jωt dt (7)
n=0 −∞
where
As simplified with T = 1, time sample N is equal to k
frequency, therefore resulting as following: w(t) = window function
x(t) = the signal to be transformed
H(k) = h(n)e, k = 0,1,2,...,N-1 (4)
X(τ, ω) = essentially the Fourier Transform of x(t)w(t − τ)
2
3. τ = freqency axis According to Theory of Shannon, the minimum value
ω = variable to suppress any jump discontinuity of sampling frequency is more or less half times of the
signal frequency. Thus, the sampling yields original
shapes of signal. The greater is better, as it visualizes
The usual mathematical definition of the discrete- authentic signal.
time STFT is: The following figure 3 shows the sampling process
∞
in the analog and digital signals.
Xm (ω) = x(n)w(n − mR)e− jωn (8)
n=−∞
= DTFTω (x.ShiftmR (w)), (9)
where
x(n) = input signal at time n
w(n) = length M window function (e.g. Hamming)
Xm (ω) = DTFT of windowed data centered about
time mR
Figure 3. Sampling process
R = hop size, in samples, between successive
DTFTs. 2.3.2 Frame Blocking
whereas: τ is time parameter, ω is frequency parame- Frame-blocking is a method to divide sound signal
ter, x(t) is analyzed signal, W(t-τ) is window function into several frames. In one frame consists of several
and e− jωt dt is inherited function from Discrete Fourier samples. Capturing samples depends on quantity of
Transform. sounds in every second and the magnitude of sam-
Analyzing signal is described in following dia- pling frequency. Described as following figure 4.
gram.
Input signals Sampling
Frame blocking
Figure 4. Signal in Frame-blocking
2.3.3 Windowing
Windowing Sliced signals in every frame are prone to data errors
FFT
when calculated through Fourier transforming. Thus,
windowing is necessary to reduce discontinuity effects
in sliced signals. In simple calculation of continuous
signal, transformation is taken place with multiplying
Notes every short-time signal with window function in period
of time.
figure 2. Signal Block Diagram In this phase, frequency scaling is measured only
in length of window. As the output from the previous
2.3.1 Sampling Process phases that produced by STFT function in frequency
and time integrated with windowing, generating visual
The sound signal is analogous or continuous and cat- content of tones.
egorized as infinite time interval. As an object of ob-
servation, sound is partitioned into slices in time con-
straints. Therefore, so-called as finite time interval. 3 Analysis and Testing
Based on theory of Nyquist, sampling frequency is
required at least twice times signal frequency: Performance testing and durability are examined
with 3 sound files: SaronTok.wav, consisting of notes
Fsampling ≥ 2 × Fsignal (10) of saron; SaronDemung.wav, consisting of notes of
3
4. saron and demung; SarongBonang.wav, consisting of
notes of saron and bonang. Three kinds of different
length of window are inspected: 2048, 4096 and 8192.
Extracting tones of saron in SaronTok.wav with
length of window 2048 is shown in figure 5.
Figure 8. Intersections between saron with bonang
The experiment is not fully capable to analyze sig-
nals with composition of notes and in similar fre-
quency. The percentages of testing results in Saron-
Tok.wav, SaronDemung.wav, and SaronBonang.wav
are described in the following table 2.
Figure 5. Extracting tones of saron with length of
window 2048
Extracting tones of saron in SaronTok.wav with length Window Saron Saron+Demung Saron+Bonang
of window 4096 is shown in figure 6. 2048 100% 93.75% 42%
4096 100% 93.75% 50%
8192 100% 100% 57%
Table 2. Results of testing tones of saron tones in several
windows
4 Conclusion
From testing and systems analysis have been done
on the determination of the gamelan notation can be
summarized as followings:
Figure 6. Extracting tones of saron with length of
window 4096 1. In determination of the width of the window af-
Extracting tones of saron in SaronTok.wav with length fects the accuracy of the analysis, the larger the
of window 8192 is shown in figure 7. window width, different frequencies in scaling
the smaller, more meticulous and graphic signals
the ramps. While in the area when the oppo-
site occurs, the greater width of the window, the
graph in the region increasingly narrower time,
the timing of notes tends to overlap. At ampli-
tude axis, the greater width of window, more
meticulous the value.
2. In determination of blended notes of saron and
demung, yet the extraction does work well due
to dissimilarities of both notations.
3. In determination of blended notes of saron and
bonang, the extraction of both notes is arduous to
highly percentages of success due to their simil-
Figure 7. Extracting tones of saron with length of
ities in frequencies.
window 8192
In testing signals in SaronBonang.wav, some inter- 4. The highest peak frequency of saron tones is
ventions of intersection between saron and bonang in- highly influential in the accuracy of analysis in
struments, as shown in figure 8. order to determine the notations.
4
5. 5. Theoritically, this research is useful as manual to 6 Students Profile
determine other notes in other gamelan instru-
ments. Eric Jansen is student of
Computer Engineering and
Telematics, Department of
5 References Electrical Engineering,
Faculty of Industrial Tech-
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5