This technical note explains how you can very easily use the command line functions available in
the MATLAB signal processing toolbox, to simulate simple multirate DSP systems. The focus
here is to be able to view in the frequency domain what is happening at each stage of a system
involving upsamplers, downsamplers, and lowpass filters. All computations will be performed
using MATLAB and the signal processing toolbox. These same building blocks are available in
Simulink via the DSP blockset. The DSP blockset allows better visualization of the overall system,
but is not available in the ECE general computing laboratory or on most personal systems. A
DSP block set example will be included here just so one can see the possibilities with the additional
MATLAB tools.
This document summarizes an audio noise cancellation project. It outlines the project schedule, methods used including decoding audio files, applying fast Fourier transforms (FFTs) and inverse FFTs (IFFTs), and developing algorithms to filter noise and find suitable noise profiles to subtract. It discusses challenges faced with data types, filter design, and implementing the inverse FFT. The overall goal is to develop techniques to remove noise from audio signals.
This document provides an overview of decimation and interpolation in multirate signal processing. It discusses downsampling by an integer factor M, which reduces the sampling rate by taking every M-th sample and discarding the rest. Downsampling can cause aliasing if the signal is not bandlimited, so a low-pass filter is used beforehand. The document also covers properties like linearity and time-variance, identities for cascading systems, and polyphase decomposition to more efficiently implement decimation filters when the number of coefficients is a multiple of the decimation factor. Examples and illustrations are provided using MATLAB code.
An introductory presentation covered key concepts in deep learning including neural networks, activation functions, cost functions, and optimization methods. Popular deep learning frameworks TensorFlow and tensorflow.js were discussed. Common deep learning architectures like convolutional neural networks and generative adversarial networks were explained. Examples and code snippets in Python demonstrated fundamental deep learning concepts.
Introduction to Deep Learning, Keras, and TensorflowOswald Campesato
A fast-paced introduction to Deep Learning concepts, such as activation functions, cost functions, back propagation, and then a quick dive into CNNs. Basic knowledge of vectors, matrices, and derivatives is helpful in order to derive the maximum benefit from this session. Then we'll see how to create a Convolutional Neural Network in Keras, followed by a quick introduction to TensorFlow and TensorBoard.
This document discusses the TMS320C6713 digital signal processor (DSP) development kit (DSK). The DSK features the high-performance TMS320C6713 floating-point DSP chip capable of 1350 million floating point operations per second. The DSK allows for efficient development and testing of applications for the C6713 DSP. It includes onboard memory, an analog interface circuit for data conversion, I/O ports, and JTAG emulation support. The DSK also includes a stereo codec for analog audio input/output.
A fast-paced introduction to Deep Learning concepts, such as activation functions, cost functions, back propagation, and then a quick dive into CNNs, followed by a Keras code sample for defining a CNN. Basic knowledge of vectors, matrices, and derivatives is helpful in order to derive the maximum benefit from this session. Then we'll see a short introduction to TensorFlow 1.x and some insights into TF 2 that will be released some time this year.
This document describes an experiment using Matlab to represent and manipulate signals. It outlines various tasks for students to complete, including sampling signals, analyzing aliasing, visualizing signals using different commands, generating non-periodic and periodic signals like sinusoids, square waves and sawtooth waves. Students are instructed to write code, make observations, and include specific sections in their report.
This document summarizes an audio noise cancellation project. It outlines the project schedule, methods used including decoding audio files, applying fast Fourier transforms (FFTs) and inverse FFTs (IFFTs), and developing algorithms to filter noise and find suitable noise profiles to subtract. It discusses challenges faced with data types, filter design, and implementing the inverse FFT. The overall goal is to develop techniques to remove noise from audio signals.
This document provides an overview of decimation and interpolation in multirate signal processing. It discusses downsampling by an integer factor M, which reduces the sampling rate by taking every M-th sample and discarding the rest. Downsampling can cause aliasing if the signal is not bandlimited, so a low-pass filter is used beforehand. The document also covers properties like linearity and time-variance, identities for cascading systems, and polyphase decomposition to more efficiently implement decimation filters when the number of coefficients is a multiple of the decimation factor. Examples and illustrations are provided using MATLAB code.
An introductory presentation covered key concepts in deep learning including neural networks, activation functions, cost functions, and optimization methods. Popular deep learning frameworks TensorFlow and tensorflow.js were discussed. Common deep learning architectures like convolutional neural networks and generative adversarial networks were explained. Examples and code snippets in Python demonstrated fundamental deep learning concepts.
Introduction to Deep Learning, Keras, and TensorflowOswald Campesato
A fast-paced introduction to Deep Learning concepts, such as activation functions, cost functions, back propagation, and then a quick dive into CNNs. Basic knowledge of vectors, matrices, and derivatives is helpful in order to derive the maximum benefit from this session. Then we'll see how to create a Convolutional Neural Network in Keras, followed by a quick introduction to TensorFlow and TensorBoard.
This document discusses the TMS320C6713 digital signal processor (DSP) development kit (DSK). The DSK features the high-performance TMS320C6713 floating-point DSP chip capable of 1350 million floating point operations per second. The DSK allows for efficient development and testing of applications for the C6713 DSP. It includes onboard memory, an analog interface circuit for data conversion, I/O ports, and JTAG emulation support. The DSK also includes a stereo codec for analog audio input/output.
A fast-paced introduction to Deep Learning concepts, such as activation functions, cost functions, back propagation, and then a quick dive into CNNs, followed by a Keras code sample for defining a CNN. Basic knowledge of vectors, matrices, and derivatives is helpful in order to derive the maximum benefit from this session. Then we'll see a short introduction to TensorFlow 1.x and some insights into TF 2 that will be released some time this year.
This document describes an experiment using Matlab to represent and manipulate signals. It outlines various tasks for students to complete, including sampling signals, analyzing aliasing, visualizing signals using different commands, generating non-periodic and periodic signals like sinusoids, square waves and sawtooth waves. Students are instructed to write code, make observations, and include specific sections in their report.
This document provides information about an expert systems and solutions company located in Paiyanoor, Chennai that works with students on research projects. The company has labs where students can assemble hardware and receive guidance from experts. They are looking for final year students and Ph.D students from electrical and electronics fields to work on projects.
This document discusses decimation and interpolation using polyphase filters. It begins by defining decimation and interpolation and describing how decimators use anti-aliasing filters followed by downsamplers, while interpolators use upsamplers followed by anti-imaging filters. It then presents the principles of polyphase decimation and interpolation, showing how they can be represented in both the time and z-transform domains. This allows implementing decimators and interpolators more efficiently using fewer filter operations and less memory than traditional implementations.
DSP_FOEHU - Lec 08 - The Discrete Fourier TransformAmr E. Mohamed
The document discusses the Discrete Fourier Transform (DFT). It explains that while the discrete-time Fourier transform (DTFT) and z-transform are not numerically computable, the DFT avoids this issue. The DFT represents periodic sequences as a sum of complex exponentials with frequencies that are integer multiples of the fundamental frequency. It can be viewed as computing samples of the DTFT or z-transform at discrete frequency points, allowing numerical computation. The DFT provides a link between the time and frequency domain representations of a finite-length sequence.
The document discusses digital signal processing and filter design using MATLAB commands. It provides examples of designing low pass, high pass, and band pass filters using commands like Filter(), FILT(), TF(), and ZPK(). Low pass filters pass low frequencies and attenuate high frequencies. High pass filters do the opposite. Band pass filters pass a range of frequencies and reject others. The document demonstrates designing each filter type and applying the filters to sample signals.
The document describes an experiment to verify the Nyquist sampling theorem using MATLAB. It discusses sampling a continuous time signal at frequencies below, equal to, and above twice the maximum frequency of the signal. The results show aliasing when sampling below the Nyquist rate, no aliasing when sampling at the Nyquist rate, and perfect reconstruction when sampling above the Nyquist rate. The experiment generates a sinusoidal signal, samples it at different rates, and plots the discrete and reconstructed continuous signals to demonstrate the sampling theorem.
This document provides an overview and introduction to TensorFlow 2. It discusses major changes from TensorFlow 1.x like eager execution and tf.function decorator. It covers working with tensors, arrays, datasets, and loops in TensorFlow 2. It also demonstrates common operations like arithmetic, reshaping and normalization. Finally, it briefly introduces working with Keras and neural networks in TensorFlow 2.
DSP_FOEHU - Lec 09 - Fast Fourier TransformAmr E. Mohamed
The document discusses the Fast Fourier Transform (FFT) algorithm. It explains that the FFT decomposes an N-point discrete Fourier transform (DFT) into smaller DFTs of size N/2, taking advantage of the periodicity and symmetry of complex numbers. For N that is a power of 2, it separates the input sequence into even and odd indexed parts, then recursively applies this decomposition until 2-point DFTs are reached. This decimation-in-time approach reduces the computational complexity from O(N^2) for the direct DFT to O(NlogN) for the FFT.
This session for beginners introduces tf.data APIs for creating data pipelines by combining various "lazy operators" in tf.data, such as filter(), map(), batch(), zip(), flatmap(), take(), and so forth.
Familiarity with method chaining and TF2 is helpful (but not required). If you are comfortable with FRP, the code samples in this session will be very familiar to you.
The document contains the laboratory manual for the digital signal processing lab of Jayalakshmi Institute of Technology. It lists the experiments to be conducted using MATLAB and TMS320C5416. The experiments using MATLAB include generation of discrete time signals, verification of sampling theorem, calculation of FFT and IFFT, analysis of LTI systems, convolution, and design of FIR and IIR filters. The experiments using TMS320C5416 include linear and circular convolution, calculation of FFT, generation of signals, and implementation of FIR and IIR filters. Detailed procedures and programs are provided for each experiment.
This document contains an index of 10 experiments related to signal processing using MATLAB. It lists the aim, page numbers, and brief description of each experiment. The experiments include developing basic signals, performing operations on sequences like addition and multiplication, linear convolution, impulse response of systems, Z-transform, Fourier transform, and finding the magnitude and phase response of linear time-invariant systems. Sample MATLAB code and generated waveforms are provided for some of the experiments.
Digital Signal Processing Lab Manual ECE studentsUR11EC098
This document describes a MATLAB program to perform operations on discrete-time signals. It discusses amplitude manipulation operations like amplification, attenuation, and amplitude reversal. Time manipulation operations covered include time shifting and time reversal. It also describes adding and multiplying two discrete signals. The program takes user input, performs the selected operations, and plots the output waveforms to verify results.
A Simple Communication System Design Lab #4 with MATLAB SimulinkJaewook. Kang
This document outlines a communication systems design lab using MATLAB Simulink. It discusses implementing various components of a communication system including channels, phase splitters, up/down conversion, and more. The lab covers how to build subsystems, use MATLAB functions in Simulink, and bring variables from the workspace. The goal is to complete a target communication system by implementing a channel model using Simulink blocks, MATLAB functions, and variables from the workspace.
The document provides MATLAB programs for signal processing tasks including representation of basic signals, linear and circular convolution, overlap save and overlap add methods for convolution, and crosscorrelation and autocorrelation. It includes MATLAB code to generate unit impulse, step, ramp, exponential, sine and cosine signals. Code is also provided to compute linear convolution, circular convolution with and without zero padding, and implement overlap save and overlap add methods for convolution of sequences. Crosscorrelation and autocorrelation code is given as well.
Effects of varying number of samples in an imagelakshmymk
The document discusses the effect of varying the number of samples on image quality through upsampling and downsampling. It shows how downsampling an image by omitting pixel values reduces the image resolution and quality. In contrast, upsampling does not remove pixel values but instead interpolates new values, so downsampling the upsampled image back to the original size nearly recovers the original quality. The key factors are that downsampling removes information while upsampling preserves information through interpolation.
Matlab code for comparing two microphone filesMinh Anh Nguyen
This MATLAB code reads in two audio files, extracts the right channel of the stereo signal, cuts both signals to the same length, and performs several analyses to compare the signals:
1. It plots the cut signals and their FFTs to visually compare them.
2. It calculates the mean squared error (MSE) between the cut signals and determines if they are the same or not based on a threshold.
3. It calculates various digital statistics of the cut signals like mean, standard deviation, variance, and average power and displays them.
4. It performs a cross-correlation between the FFTs of the cut signals and plots the result.
The document describes MATLAB software and its uses for signal processing. MATLAB is a matrix-based program for scientific and engineering computation. It provides built-in functions for technical computation, graphics, and animation. The Signal Processing Toolbox contains functions for filtering, Fourier transforms, convolution, and filter design. The document lists some important MATLAB commands and frequently used signal processing functions, along with their syntax and purpose. It also describes the basic windows of the MATLAB interface and provides examples of generating common continuous and discrete time signals using MATLAB code.
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.
DSP_FOEHU - Lec 03 - Sampling of Continuous Time SignalsAmr E. Mohamed
1. The Nyquist interval is the longest time interval that can be used for sampling a bandlimited signal while still allowing reconstruction of the signal without distortion.
2. The sampling theorem states that a signal x(t) with finite energy can be reconstructed from its sampled values x(nTs) if the sampling frequency is greater than twice the maximum frequency of the signal.
3. Reconstruction of a sampled signal involves representing the sampled signal as a sum of sinusoids with frequencies that are integer multiples of the sampling frequency below the Nyquist frequency.
A Simple Communication System Design Lab #3 with MATLAB SimulinkJaewook. Kang
This document outlines the schedule and topics for a series of labs on communication system design using MATLAB Simulink. The upcoming Lab #3 will cover phase splitting, which extracts the real and imaginary components from a complex baseband signal, and up/down conversion, which shifts signals between baseband and intermediate frequencies. The lab is scheduled for April 1st from 1-4pm and will be instructed by Jaewook Kang. Previous and future labs will cover topics like OFDM, S-function design, channel modeling, and subsystem implementation.
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.
The document describes implementing the linear convolution of two sequences using MATLAB. Linear convolution involves reflecting one sequence, shifting it, multiplying the sequences element-wise, and summing the results. An example calculates the output of convolving the sequences [1, 2, 3, 1] and [1, 1, 1], yielding the output sequence [1, 3, 6, 6, 4].
EC8553 Discrete time signal processing ssuser2797e4
This document contains a 10 question, multiple choice exam on discrete time signal processing. It covers topics like the discrete Fourier transform (DFT), finite word length effects, fixed point vs floating point representation, and FIR filter design. Specifically, it includes questions that calculate the 4 point DFT of a sequence, define twiddle factors, compare DIT and DIF FFT algorithms, and discuss stability and causality of systems.
This document provides information about an expert systems and solutions company located in Paiyanoor, Chennai that works with students on research projects. The company has labs where students can assemble hardware and receive guidance from experts. They are looking for final year students and Ph.D students from electrical and electronics fields to work on projects.
This document discusses decimation and interpolation using polyphase filters. It begins by defining decimation and interpolation and describing how decimators use anti-aliasing filters followed by downsamplers, while interpolators use upsamplers followed by anti-imaging filters. It then presents the principles of polyphase decimation and interpolation, showing how they can be represented in both the time and z-transform domains. This allows implementing decimators and interpolators more efficiently using fewer filter operations and less memory than traditional implementations.
DSP_FOEHU - Lec 08 - The Discrete Fourier TransformAmr E. Mohamed
The document discusses the Discrete Fourier Transform (DFT). It explains that while the discrete-time Fourier transform (DTFT) and z-transform are not numerically computable, the DFT avoids this issue. The DFT represents periodic sequences as a sum of complex exponentials with frequencies that are integer multiples of the fundamental frequency. It can be viewed as computing samples of the DTFT or z-transform at discrete frequency points, allowing numerical computation. The DFT provides a link between the time and frequency domain representations of a finite-length sequence.
The document discusses digital signal processing and filter design using MATLAB commands. It provides examples of designing low pass, high pass, and band pass filters using commands like Filter(), FILT(), TF(), and ZPK(). Low pass filters pass low frequencies and attenuate high frequencies. High pass filters do the opposite. Band pass filters pass a range of frequencies and reject others. The document demonstrates designing each filter type and applying the filters to sample signals.
The document describes an experiment to verify the Nyquist sampling theorem using MATLAB. It discusses sampling a continuous time signal at frequencies below, equal to, and above twice the maximum frequency of the signal. The results show aliasing when sampling below the Nyquist rate, no aliasing when sampling at the Nyquist rate, and perfect reconstruction when sampling above the Nyquist rate. The experiment generates a sinusoidal signal, samples it at different rates, and plots the discrete and reconstructed continuous signals to demonstrate the sampling theorem.
This document provides an overview and introduction to TensorFlow 2. It discusses major changes from TensorFlow 1.x like eager execution and tf.function decorator. It covers working with tensors, arrays, datasets, and loops in TensorFlow 2. It also demonstrates common operations like arithmetic, reshaping and normalization. Finally, it briefly introduces working with Keras and neural networks in TensorFlow 2.
DSP_FOEHU - Lec 09 - Fast Fourier TransformAmr E. Mohamed
The document discusses the Fast Fourier Transform (FFT) algorithm. It explains that the FFT decomposes an N-point discrete Fourier transform (DFT) into smaller DFTs of size N/2, taking advantage of the periodicity and symmetry of complex numbers. For N that is a power of 2, it separates the input sequence into even and odd indexed parts, then recursively applies this decomposition until 2-point DFTs are reached. This decimation-in-time approach reduces the computational complexity from O(N^2) for the direct DFT to O(NlogN) for the FFT.
This session for beginners introduces tf.data APIs for creating data pipelines by combining various "lazy operators" in tf.data, such as filter(), map(), batch(), zip(), flatmap(), take(), and so forth.
Familiarity with method chaining and TF2 is helpful (but not required). If you are comfortable with FRP, the code samples in this session will be very familiar to you.
The document contains the laboratory manual for the digital signal processing lab of Jayalakshmi Institute of Technology. It lists the experiments to be conducted using MATLAB and TMS320C5416. The experiments using MATLAB include generation of discrete time signals, verification of sampling theorem, calculation of FFT and IFFT, analysis of LTI systems, convolution, and design of FIR and IIR filters. The experiments using TMS320C5416 include linear and circular convolution, calculation of FFT, generation of signals, and implementation of FIR and IIR filters. Detailed procedures and programs are provided for each experiment.
This document contains an index of 10 experiments related to signal processing using MATLAB. It lists the aim, page numbers, and brief description of each experiment. The experiments include developing basic signals, performing operations on sequences like addition and multiplication, linear convolution, impulse response of systems, Z-transform, Fourier transform, and finding the magnitude and phase response of linear time-invariant systems. Sample MATLAB code and generated waveforms are provided for some of the experiments.
Digital Signal Processing Lab Manual ECE studentsUR11EC098
This document describes a MATLAB program to perform operations on discrete-time signals. It discusses amplitude manipulation operations like amplification, attenuation, and amplitude reversal. Time manipulation operations covered include time shifting and time reversal. It also describes adding and multiplying two discrete signals. The program takes user input, performs the selected operations, and plots the output waveforms to verify results.
A Simple Communication System Design Lab #4 with MATLAB SimulinkJaewook. Kang
This document outlines a communication systems design lab using MATLAB Simulink. It discusses implementing various components of a communication system including channels, phase splitters, up/down conversion, and more. The lab covers how to build subsystems, use MATLAB functions in Simulink, and bring variables from the workspace. The goal is to complete a target communication system by implementing a channel model using Simulink blocks, MATLAB functions, and variables from the workspace.
The document provides MATLAB programs for signal processing tasks including representation of basic signals, linear and circular convolution, overlap save and overlap add methods for convolution, and crosscorrelation and autocorrelation. It includes MATLAB code to generate unit impulse, step, ramp, exponential, sine and cosine signals. Code is also provided to compute linear convolution, circular convolution with and without zero padding, and implement overlap save and overlap add methods for convolution of sequences. Crosscorrelation and autocorrelation code is given as well.
Effects of varying number of samples in an imagelakshmymk
The document discusses the effect of varying the number of samples on image quality through upsampling and downsampling. It shows how downsampling an image by omitting pixel values reduces the image resolution and quality. In contrast, upsampling does not remove pixel values but instead interpolates new values, so downsampling the upsampled image back to the original size nearly recovers the original quality. The key factors are that downsampling removes information while upsampling preserves information through interpolation.
Matlab code for comparing two microphone filesMinh Anh Nguyen
This MATLAB code reads in two audio files, extracts the right channel of the stereo signal, cuts both signals to the same length, and performs several analyses to compare the signals:
1. It plots the cut signals and their FFTs to visually compare them.
2. It calculates the mean squared error (MSE) between the cut signals and determines if they are the same or not based on a threshold.
3. It calculates various digital statistics of the cut signals like mean, standard deviation, variance, and average power and displays them.
4. It performs a cross-correlation between the FFTs of the cut signals and plots the result.
The document describes MATLAB software and its uses for signal processing. MATLAB is a matrix-based program for scientific and engineering computation. It provides built-in functions for technical computation, graphics, and animation. The Signal Processing Toolbox contains functions for filtering, Fourier transforms, convolution, and filter design. The document lists some important MATLAB commands and frequently used signal processing functions, along with their syntax and purpose. It also describes the basic windows of the MATLAB interface and provides examples of generating common continuous and discrete time signals using MATLAB code.
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.
DSP_FOEHU - Lec 03 - Sampling of Continuous Time SignalsAmr E. Mohamed
1. The Nyquist interval is the longest time interval that can be used for sampling a bandlimited signal while still allowing reconstruction of the signal without distortion.
2. The sampling theorem states that a signal x(t) with finite energy can be reconstructed from its sampled values x(nTs) if the sampling frequency is greater than twice the maximum frequency of the signal.
3. Reconstruction of a sampled signal involves representing the sampled signal as a sum of sinusoids with frequencies that are integer multiples of the sampling frequency below the Nyquist frequency.
A Simple Communication System Design Lab #3 with MATLAB SimulinkJaewook. Kang
This document outlines the schedule and topics for a series of labs on communication system design using MATLAB Simulink. The upcoming Lab #3 will cover phase splitting, which extracts the real and imaginary components from a complex baseband signal, and up/down conversion, which shifts signals between baseband and intermediate frequencies. The lab is scheduled for April 1st from 1-4pm and will be instructed by Jaewook Kang. Previous and future labs will cover topics like OFDM, S-function design, channel modeling, and subsystem implementation.
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.
The document describes implementing the linear convolution of two sequences using MATLAB. Linear convolution involves reflecting one sequence, shifting it, multiplying the sequences element-wise, and summing the results. An example calculates the output of convolving the sequences [1, 2, 3, 1] and [1, 1, 1], yielding the output sequence [1, 3, 6, 6, 4].
EC8553 Discrete time signal processing ssuser2797e4
This document contains a 10 question, multiple choice exam on discrete time signal processing. It covers topics like the discrete Fourier transform (DFT), finite word length effects, fixed point vs floating point representation, and FIR filter design. Specifically, it includes questions that calculate the 4 point DFT of a sequence, define twiddle factors, compare DIT and DIF FFT algorithms, and discuss stability and causality of systems.
The document describes experiments conducted in MATLAB to visualize and understand various continuous-time and discrete-time signals. In experiment 1, common continuous signals like unit step, ramp, impulse etc. are plotted. Experiment 2 involves plotting corresponding discrete-time signals. The document provides MATLAB code examples to generate and plot these standard signals.
This document discusses and compares filter banks and Mel-Frequency Cepstral Coefficients (MFCCs) for speech processing in machine learning applications. It explains that both methods involve framing a speech signal, applying a Fourier transform to obtain the power spectrum, and then extracting features using filters. For MFCCs, the filters are applied on a Mel scale and then a discrete cosine transform is used to decorrelate the coefficients. While MFCCs were popular for older models, filter banks are becoming more common for deep learning as the models can handle correlated inputs better. In the end, filter banks are recommended if the model isn't sensitive to correlation, while MFCCs remain useful if the model is sensitive to correlated
This document discusses using a C8051 MCU to calculate FFTs in real-time for audio spectrum analysis. It introduces:
(1) Key techniques used in the FFT software to optimize efficiency and accuracy, including avoiding multiplications, 16-bit integer storage, and using the MCU's on-chip PLL.
(2) The FFT algorithm and techniques like bit-reversal, windowing and anti-aliasing filtering.
(3) Details of the software design and implementation, including interrupt service routines to read ADC samples, windowing functions, bit-reversal indexing, and FFT computation loops.
(4) Experimental results analyzing the performance under different configurations and analyzing properties like
The document discusses various image filtering techniques in the frequency domain. It begins by introducing convolution as frequency domain filtering using the Fourier transform. It then provides examples of low pass and high pass filtering using sharp cut-off and Gaussian filters. Additional topics covered include the Butterworth filter, homomorphic filtering to separate illumination and reflectance, and systematic design of 2D finite impulse response (FIR) filters.
This lab report describes reconstructing a sampled signal to its original continuous time signal. The students implemented the discrete time Fourier transform (DTFT) to reconstruct the signal using different reconstruction time periods. Decreasing the reconstruction frequency from the sampling frequency resulted in a reconstructed signal that differed from the original. The students analyzed the reconstruction process and effects of varying the reconstruction frequency relative to the sampling frequency.
The smallest positive guess for which the Newton method diverges for the function f(x)=atan(x) is 1.4. The Newton method was able to find the root for guesses up to 1.39 but produced a divide by zero error at 1.4, indicating that 1.4 is the smallest positive value where the method diverges.
This document provides an overview of digital filter design. It introduces finite impulse response (FIR) and infinite impulse response (IIR) filters. FIR filters are designed using window techniques like rectangular, Hamming, and Kaiser windows. IIR filters are designed using approximation methods like Butterworth, Chebyshev I, and Chebyshev II. MATLAB code is provided to design low pass, high pass, and other filters using different window and approximation techniques. Pros and cons of FIR and IIR filters are discussed along with references.
Applied Digital Signal Processing 1st Edition Manolakis Solutions Manualtowojixi
Full download http://alibabadownload.com/product/applied-digital-signal-processing-1st-edition-manolakis-solutions-manual/
Applied Digital Signal Processing 1st Edition Manolakis Solutions Manual
The document presents an adaptive noise cancellation system for removing noise from audio signals. It uses an adaptive filter based on the least mean square (LMS) algorithm to filter noise from a noisy audio input signal. The adaptive filter adjusts its coefficients over time to minimize the error between the filter output and the clean audio signal. The system was implemented in MATLAB and produced output waveforms showing the clean audio signal, noisy input, filter output, and error signal. The adaptive noise cancellation system was found to efficiently remove noise from audio signals.
This chapter discusses modeling ideal data converters like ADCs and DACs using SPICE behavioral elements. This allows analyzing mixed-signal circuit performance through SPICE simulation more efficiently. Behavioral models are generated for ideal ADCs and DACs. Sampling a signal replicates its spectrum at intervals of the sampling frequency, which can cause aliasing. SPICE is used to analyze signals in the frequency domain to study the effects of conversion. Ideal anti-aliasing and reconstruction filters are discussed, which should have linear phase and a cutoff frequency of half the sampling rate.
Frequency Response with MATLAB Examples.pdfSunil Manjani
The document discusses frequency response analysis and control system design. It introduces frequency response, defines it as the steady-state response of a system to a sinusoidal input in terms of gain and phase lag. Bode diagrams are presented as a tool to graphically analyze the frequency response from a transfer function or experimentally. MATLAB functions like tf() and bode() are used to define transfer functions and plot Bode diagrams from the frequency response. Discrete-time PID and PI controller implementations and state-space models are also covered.
This document provides Matlab code examples for modeling various receiver non-idealities including additive white Gaussian noise, carrier frequency offset, phase noise, I/Q imbalances, automatic gain control, sampling clock offset, and clipping and quantization. The code shows how to apply these non-idealities to an input signal in sequence to generate a simulated received signal. Parameters for each non-ideality can be configured and the code outputs both the processed signal and information about the non-ideality parameters.
The document provides an introduction to digital signal processing (DSP) algorithms and architecture. It discusses key topics including DSP systems, sampling processes, discrete Fourier transforms, linear time-invariant systems, digital filters, and decimation and interpolation. The learning objectives are to understand these fundamental DSP concepts and use MATLAB as an analysis and design tool. The contents cover DSP systems, sampling, the discrete Fourier transform and fast Fourier transform, linear time-invariant systems, digital filters, and decimation and interpolation. Textbooks and references on the subject are also listed.
The document describes experiments conducted in a digital signal processing lab to implement various modulation techniques and filter designs using MATLAB. In experiment 1, programs are created to generate AM, FM and PWM modulated waves. Experiment 2 involves writing a program for linear convolution of sequences. Experiment 3 develops FIR filter programs. Experiments 4 and 5 create Butterworth and Chebyshev IIR filter designs respectively and obtain their frequency responses.
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Experiment C.1 tests examples C.1 to C.11 by:
1. Moving a 23-bit constant to the extended data-page pointer register using direct addressing mode.
2. Loading the accumulator register with data from an address pointed to by an auxiliary register using indirect addressing mode.
3. Loading the accumulator register with two words from addresses pointed to by two auxiliary registers using dual indirect addressing mode.
Design and Implementation of Low Ripple Low Power Digital Phase-Locked LoopCSCJournals
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IEEE Aerospace and Electronic Systems Society as a Graduate Student Member
Multirate sim
1. Introduction 1
Multirate Sampling Simulation Using
MATLAB’s Signal Processing Toolbox
Introduction
This technical note explains how you can very easily use the command line functions available in
the MATLAB signal processing toolbox, to simulate simple multirate DSP systems. The focus
here is to be able to view in the frequency domain what is happening at each stage of a system
involving upsamplers, downsamplers, and lowpass filters. All computations will be performed
using MATLAB and the signal processing toolbox. These same building blocks are available in
Simulink via the DSP blockset. The DSP blockset allows better visualization of the overall sys-
tem, but is not available in the ECE general computing laboratory or on most personal systems. A
DSP block set example will be included here just so one can see the possibilities with the addi-
tional MATLAB tools.
Command Line Building Blocks
To be able to visualize the spectra in a multirate system we need the basic building blocks of
• Bandlimited signal generation; here we create a signal with a triangle shaped spectrum using
sinc()
• Integer upsampling and downsampling operations; here we use the signal processing tool-
box functions upsample() and downsample()
• Lowpass filtering for antialiasing and interpolation; here we use fir1()
• If we don’t care to examine the spectra between the antialiasing lowpass filter and the deci-
mator or between the upsampler and interpolation filter, we can use combination functions
such as decimate(), interpolate(), and resample()
Signal Generation
In a theoretical discussion of sampling theory it is common place to represent the signal of interest
as having a triangular shaped Fourier spectrum. Another common signal type is one or more dis-
crete-time sinusoids. We know that
(1)
where
ωcnsin
πn
-----------------
ω
2ωc
---------
∏↔
F
x
W 2⁄W 2⁄–
1x
W
-----
∏ = W
2. ECE 5650/4650 Simulation with MATLAB
Command Line Building Blocks 2
A triangle can be obtained in the frequency domain by noting that
(2)
The periodic convolution on the right-side of (2) yields
where is the spectral bandwidth (single-sided or lowpass) in normalized frequency units. It
then follows that for a unit height spectrum we have the transform pair
(3)
where
Using the sinc( ) function in MATLAB, which is defined as
(4)
we can write (3) as
(5)
Creating a triangular spectrum signal in MATLAB just requires delaying the signal in samples so
that both tails can be represented in a causal simulation, e.g.,
>> n = 0:1024;
>> x = 1/4*sinc(1/4*(n-512)).^2; % set peak of signal to center of interval
>> f = -1:1/512:1; % create a custom frequency axis for spectral plotting
>> X = freqz(x,1,2*pi*f); %Compute the Fourier transform of x
>> plot(f,abs(X))
>> print -tiff -depsc multi1.eps
ωcn 2⁄( )sin
πn
-----------------------------
2
1
2π
------
ω θ–
ωc
-------------
θ
ωc
------
∏∏ θd
π–
π
∫↔
F
ω
ωcω– c
ωc
2π
------ fc=
fc
2π
ωc
------
ωcn 2⁄( )sin
πn
-----------------------------
2
Λ
ω
ωc
------
↔
F
x
WW–
1
Λ
x
W
-----
=
sinc x( )
πxsin
πx
--------------≡
fc sinc fcn( )[ ]
2
Λ
ω
2πfc
----------
↔
F
3. ECE 5650/4650 Simulation with MATLAB
Command Line Building Blocks 3
Consider a couple of more examples:
>> n = 0:1024;
>> x125 = 1/8*sinc(1/8*(n-512)).^2;
>> x5 = 1/2*sinc(1/2*(n-512)).^2;
>> f = -1:1/512:1;
>> X125 = freqz(x125,1,2*pi*f);
>> X5 = freqz(x5,1,2*pi*f);
>> subplot(211)
>> plot(f,abs(X125))
>> subplot(212)
>> plot(f,abs(X5))
>> print -tiff -depsc multi2.eps
Upsample and Downsample
With a means to generate a signal having bandlimited spectra in place, we can move on to the
upsampling and downsampling operations. The signal processing toolbox has dedicated functions
for doing this operation, although they are actually quite easy to write yourself.
>> help downsample
−1 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 1
0
0.2
0.4
0.6
0.8
1
Normalized Frequency
ω
2π
------
X e
jω
( )
fc 0.25 or ωc
π
2
---= =
−1 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 1
0
0.5
1
−1 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 1
0
0.5
1
Normalized Frequency
ω
2π
------
X e
jω
( )
X e
jω
( )
ωc
π
4
---=
ωc π=
4. ECE 5650/4650 Simulation with MATLAB
Command Line Building Blocks 4
DOWNSAMPLE Downsample input signal.
DOWNSAMPLE(X,N) downsamples input signal X by keeping every
N-th sample starting with the first. If X is a matrix, the
downsampling is done along the columns of X.
DOWNSAMPLE(X,N,PHASE) specifies an optional sample offset.
PHASE must be an integer in the range [0, N-1].
See also UPSAMPLE, UPFIRDN, INTERP, DECIMATE, RESAMPLE.
>> help upsample
UPSAMPLE Upsample input signal.
UPSAMPLE(X,N) upsamples input signal X by inserting
N-1 zeros between input samples. X may be a vector
or a signal matrix (one signal per column).
UPSAMPLE(X,N,PHASE) specifies an optional sample offset.
PHASE must be an integer in the range [0, N-1].
See also DOWNSAMPLE, UPFIRDN, INTERP, DECIMATE, RESAMPLE.
These functions will be used in examples that follow.
Filtering
To implement a simple yet effective lowpass filter to prevent aliasing in a downsampler and inter-
polation in an upsampler, we can use the function fir1() which designs linear phase FIR filters
using a windowed sinc function.
>> help fir1
FIR1 FIR filter design using the window method.
B = FIR1(N,Wn) designs an N'th order lowpass FIR digital filter
and returns the filter coefficients in length N+1 vector B.
The cut-off frequency Wn must be between 0 < Wn < 1.0, with 1.0
corresponding to half the sample rate. The filter B is real and
has linear phase. The normalized gain of the filter at Wn is
-6 dB.
More help beyond this, but this is the basic LPF design interface
The filter design functions use half sample rate normalized frequencies:
ω
f′
π 2π
10
Input on f′ axis
π M⁄
1 M⁄
To get this,
enter this
5. ECE 5650/4650 Simulation with MATLAB
System Simulation 5
To design a lowpass filter FIR filter having 128 coefficients and a cutoff frequency of ,
we simply type
>> h = fir1(128-1,1/3); % Input cutoff as 2*fc, where fc = wc/(2pi)
>> freqz(h,1,512,1)
>> print -tiff -depsc multi3.eps
System Simulation
To keep things simple we will consider just simple decimator and interpolator systems.
A Simple Decimation Example
In the above system we will consider the pure decimator and the decimator with lowpass prefilter-
ing. Two different values of M will be considered.
As a first example we pass directly into an decimator with a signal having
( ).
>> n = 0:1024;
ωc π 3⁄=
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
−6000
−4000
−2000
0
Frequency (Hz)
Phase(degrees)
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
−80
−60
−40
−20
0
Frequency (Hz)
Magnitude(dB)
Mx n[ ] y n[ ]
Lowpass
ωc
π
M
-----=
ω
ωNω– N
1X e
jω
( )
Bypass LPF
M 2=
ωN π 2⁄= fN 1 4⁄=
6. ECE 5650/4650 Simulation with MATLAB
System Simulation 6
>> x = 1/4*sinc(1/4*(n-512)).^2;
>> y = downsample(x,2);
>> f = -1:1/512:1;
>> X = freqz(x,1,2*pi*f);
>> Y = freqz(y,1,2*pi*f);
>> plot(f,abs(X))
>> subplot(211)
>> plot(f,abs(X))
>> subplot(212)
>> plot(f,abs(Y))
>> print -tiff -depsc multi4.eps
• The results are exactly as we would expect
Now, use the same signal except with . First without the prefilter, and then include it to
avoid aliasing.
>> n = 0:1024;
>> x = 1/4*sinc(1/4*(n-512)).^2;
>> xf = filter(h,1,x);
>> yf = downsample(xf,3);
>> ynf = downsample(x,3);
>> X = freqz(x,1,2*pi*f);
>> Xf = freqz(xf,1,2*pi*f);
>> Yf = freqz(yf,1,2*pi*f);
>> Ynf = freqz(ynf,1,2*pi*f);
>> subplot(411)
−1 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 1
0
0.5
1
−1 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 1
0
0.2
0.4
0.6
0.8
Normalized Frequency
ω
2π
------
X e
jω
( )
Y e
jω
( )
L 2 Decimation, No Prefilter=
No aliasing
problems
M 3=
7. ECE 5650/4650 Simulation with MATLAB
System Simulation 7
>> plot(f,abs(X))
>> subplot(412)
>> plot(f,abs(Ynf))
>> subplot(413)
>> plot(f,abs(Xf))
>> subplot(414)
>> plot(f,abs(Yf))
>> print -tiff -depsc multi5.eps
A Simple Interpolation System
In the above system we will consider the pure upsampler and the upsampler followed by a low-
pass interpolation filter. Let and the signal have ( ).
>> n = 0:1024;
−1 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 1
0
0.5
1
−1 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 1
0
0.2
0.4
−1 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 1
0
0.5
1
−1 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 1
0
0.2
0.4
Normalized Frequency
ω
2π
------
X e
jω
( )
Yf e
jω
( )
Xf e
jω
( )
Ynf e
jω
( )
Aliasing Aliasing
Unfiltered
Input
Filtered
Input
Down by 3
w/o Filter
Output
Down by 3
with Filter
OutputShould be 0
but filter is
not ideal
Lowpass
ωc
π
3
---=3 yr n[ ]x n[ ]
yu n[ ]
ω
ωNω– N
1X e
jω
( )
L 3= ωN π 2⁄= fN 1 4⁄=
8. ECE 5650/4650 Simulation with MATLAB
A DSP Blockset Example 8
>> x = 1/4*sinc(1/4*(n-512)).^2;
>> y = upsample(x,3);
>> X = freqz(x,1,2*pi*f);
>> Y = freqz(y,1,2*pi*f);
>> h = fir1(128-1, 1/3);
>> yf = filter(h,1,y);
>> Yf = freqz(yf,1,2*pi*f);
>> subplot(311)
>> plot(f,abs(X))
>> subplot(312)
>> plot(f,abs(Y))
>> subplot(313)
>> plot(f,abs(Yf))
>> print -tiff -depsc multi6.eps
A DSP Blockset Example
What can be accomplished at the MATLAB command line using just the signal processing tool-
box, can be enhanced significantly by adding Simulink and the DSP blockset. Simulink is a block
diagram based simulation environment that sits on top of MATLAB. The DSP blockset augments
Simulink with a DSP specific block library and requires that the signal processing toolbox be
present.
−1 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 1
0
0.5
1
−1 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 1
0
0.5
1
−1 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 1
0
0.5
1
Normalized Frequency
ω
2π
------
X e
jω
( )
Yf e
jω
( )
Y e
jω
( )
Images removed
by lowpass filter
Input
Spectrum
Upsampled
by 3 Input
Interp.
Upsample
Output
9. ECE 5650/4650 Simulation with MATLAB
A DSP Blockset Example 9
As a simple example consider Text problem 4.15. The results are not shown here as they are in
the solutions to problem 4.15. A sinusoidal input can be connected (the plot currently off to the
side) or a signal vector from the MATLAB workspace can be used as the input. As shown above
the input from the workspace is a triangular spectrum signal. The upsampler and downsampler
blocks works just like the command line functions. The lowpass filter block has been designed
using a GUI filter design tool (FDA tool), but ultimately uses coefficients similar to those
obtained from MATLAB’s command line filter design tools. The To Workspace blocks allow the
signals to be exported to the MATLAB workspace for futher manipulation.
FDATool
wc = Pi/8 LPF
3
Upsample
simout2
To Workspace2
simout1
To Workspace1
simout
To Workspace
Sine Wave
simin
From
Workspace
3
Downsample
Simulation block diagram
for text problem 4.15