Digital Signal Processing: Illustration Using Python

✍ Scribed by S. Esakkirajan, T. Veerakumar, Badri N. Subudhi

• Publisher: Springer
• Year: 2023
• Tongue: English
• Leaves: 535
• Category: Library

✦ Synopsis

he objective of this book is to implement signal processing algorithms in Python. There are many open-source software packages available to implement signal processing algorithms. The reasons for choosing Python are (1) it is a general-purpose programming language that can be used for various tasks beyond scientific computing. (2) Python has an active community of developers who create and maintain a wide range of libraries and frameworks. (3) Python has become the language of choice for many Machine Learning and Deep Learning applications with powerful libraries such as TensorFlow, PyTorch, and Keras. The main aim of signal processing is to extract information from the signal. After extracting useful information, further processing, like classification of information, has to be done effectively using Machine Learning and Deep Learning libraries in Python.

In this book, Python is used as a tool to implement signal processing algorithms. Teaching Python is not the main aim of this book. Python is used as a vehicle to present concepts related to signal processing. In this book, the signals are generated, manipulated, transformed, and useful information is extracted using libraries available in Python. The Python programs used in this book are purposively made simple and illustrative. The libraries used in this book include (1) Numpy, (2) Scipy, (3) Matplotlib, etc. These libraries provide a wide range of tools and functions for performing operations like filtering, resampling, prediction, etc.

✦ Table of Contents

Preface
Motivation
Target Audience
Salient Features of the Book
Organization of the Book
Acknowledgments
Contents
About the Authors
Chapter 1: Generation of Continuous-Time Signals
1.1 Continuous-Time Signal
1.1.1 Continuous-Time Periodic Signal
1.1.2 Exponential Function
1.2 Non-stationary Signal
1.3 Non-sinusoidal Waveform
1.3.1 Square Waveform
1.3.2 Triangle and Sawtooth Waveform
1.3.3 Sinc Function
1.3.4 Pulse Signal
1.3.5 Gaussian Function
Bibliography
Chapter 2: Sampling and Quantization of Signals
2.1 Sampling of Signal
2.1.1 Violation of Sampling Theorem
2.1.2 Quantization of Signal
2.1.2.1 Mid-Tread Quantizer
2.1.3 Mid-Rise Quantizer
2.2 Non-uniform Quantization
2.3 Signal Reconstruction
2.3.1 Zero-Order Hold Interpolation
2.3.2 First-Order Hold Interpolation
2.3.3 Ideal or Sinc Interpolation
Bibliography
Chapter 3: Generation and Operation on Discrete-Time Sequence
3.1 Generation of Discrete-Time Signals
3.2 Mathematical Operation on Discrete-Time Signals
3.2.1 Amplitude Modification on DT Signal
3.2.1.1 Time Scaling Operation
3.2.1.2 Time Shifting Operation
3.2.1.3 Time Reversal Operation
3.3 Convolution
3.4 Correlation
Bibliography
Chapter 4: Discrete-Time Systems
4.1 Discrete-Time System
4.2 Representation of DT Systems
4.2.1 Difference Equation Representation of Discrete-Time Linear Time-Invariant System
4.2.2 State-Space Model of a Discrete-Time System
4.2.2.1 State-Space to Transfer Function
4.2.3 Impulse Response and Step Response of Discrete-Time System
4.2.4 Pole-Zero Plot of Discrete-Time System
4.3 Responses of Discrete-Time System
4.4 Different Representations and Response of Unit Delay Discrete-Time System
4.5 Properties of Discrete-Time System
4.5.1 Linearity Property
4.5.2 Time-Invariant and Time-Variant System
4.5.3 Causal and Non-causal System
4.5.4 Stability of Discrete-Time System
4.5.5 Invertibility of Discrete-Time System
Bibliography
Chapter 5: Transforms
5.1 Introduction to Transform
5.2 Z-Transform
5.2.1 Z-Transform of Standard Test Sequences
5.3 Inverse Z-Transform
5.4 Family of Fourier Series and Transforms
5.4.1 Continuous-Time Fourier Transform (CTFT)
5.4.2 Fourier Transform of Standard Test Signals
5.4.3 Discrete-Time Fourier Transform (DTFT)
5.4.4 Analysis of Discrete-Time LTI System Using DTFT
5.4.5 Discrete Fourier Transform
5.4.6 Properties of DFT
5.4.7 Limitations of Fourier Transform
5.5 Discrete Cosine Transform (DCT)
5.6 Short-Time Fourier Transform
5.6.1 Shortcoming of STFT
5.7 Continuous Wavelet Transform (CWT)
5.7.1 Continuous Wavelets Family
5.7.2 Drawback of CWT
5.8 Discrete Wavelet Transform
Bibliography
Chapter 6: Filter Design Using Pole-Zero Placement Method
6.1 First-Order IIR Filter
6.2 Moving Average filter
6.3 M-Point Exponentially Weighted Moving Average Filter (EWMA)
6.4 Digital Resonator
6.5 Notch Filter
6.6 All-Pass Filter
6.7 Comb Filter
6.7.1 Location of Poles and Zeros of Comb Filter
Bibliography
Chapter 7: FIR Filter Design
7.1 FIR Filter
7.2 Classification of FIR Filter
7.3 Design of FIR Filter
7.3.1 Steps in Window-Based FIR Filter Design
7.3.2 Window-Based FIR Lowpass Filter
7.3.3 Window-Based FIR Highpass Filter
7.3.4 Window-Based FIR Bandpass Filter
7.3.5 Window-Based FIR Band Reject Filter
7.3.6 Design of FIR Filter Using Built-In Function
7.3.7 Window Functions
7.4 Frequency Sampling-Based FIR Filter Design
7.5 Design of Optimal FIR filter
7.6 Applications of FIR Filter
Bibliography
Chapter 8: Infinite Impulse Response Filter
8.1 IIR Filter
8.2 Mapping Techniques in the Design of IIR Filter
8.2.1 Backward Difference Method
8.2.2 Impulse Invariant Technique
8.2.3 Bilinear Transformation Technique (BLT)
8.2.4 Matched Z-Transform Technique
8.3 Analog Frequency Transformation
8.4 Butterworth Filter
8.5 Chebyshev Filter
8.6 Chebyshev Type II IIR Filter
8.7 Elliptic Filter
Bibliography
Chapter 9: Quantization Effect of Digital Filter Coefficients
9.1 Number Representation
9.2 Fixed-Point Quantization
9.2.1 Fixed-Point Quantization by Rounding
9.2.2 Fixed-Point Quantization Using Two´s Complement Truncation
9.2.3 Fixed-Point Quantization Using Magnitude Truncation
9.3 Coefficient Quantization
9.4 Limit Cycle Oscillations
9.5 Cascade Form of a Higher Order Filters
Bibliography
Chapter 10: Multirate Signal Processing
10.1 Multirate Operators
10.1.1 Downsampling Operation
10.1.2 Upsampling Operation
10.2 Noble Identity
10.2.1 Noble Identity for Downsampling Operation
10.2.2 Noble Identity for Upsampling Operation
10.3 Polyphase Decomposition
10.4 Filter Bank
10.4.1 Two-Channel Filter Bank
10.4.2 Relationship Between Analysis and Synthesis Filters
10.4.3 Two-Channel Filter Bank Without Filters
10.4.4 Three-Channel Filter Bank Without Filters
10.5 Tree-Structured Filter Bank
10.6 Transmultiplexer
Bibliography
Chapter 11: Adaptive Signal Processing
11.1 Wiener Filter
11.1.1 Wiener Filter in Frequency Domain
11.2 Adaptive Filter
11.2.1 LMS Adaptive Filter
11.2.2 Normalized LMS Algorithm
11.2.3 Sign LMS Algorithm
11.3 RLS Algorithm
Bibliography
Chapter 12: Case Study
12.1 Case Study 1: Speech Recognition Using MFCC (Mel-Frequency Cepstral Coefficient)
12.1.1 Speaker Identification
12.1.2 Speaker Verification System
12.1.3 Mel-Frequency Cepstral Coefficient (MFCC) Feature
12.1.3.1 Pre-emphasis
12.1.3.2 Sampling and Windowing
12.1.3.3 Discrete Fourier Transform (DFT)
12.1.3.4 Mel-Frequency Bandpass Filter
12.1.3.5 Log Operation
12.1.3.6 Discrete Cosine Transform (DCT)
12.2 Case Study 2: QRS Detection in ECG Signal Using Pan-Tomkins Algorithm
12.2.1 ECG Signal Preprocessing
12.2.1.1 Bandpass filter
12.2.1.2 Derivative Process
12.2.1.3 Squaring Operation
12.2.2 Moving Window Integration
12.2.3 Fiducial Mark
12.2.4 Decision Rule Approach
12.3 Case Study 3: Power Quality Disturbance Detection
12.3.1 Generation of Power Quality Disturbance
12.3.2 Simulation of Power Quality Disturbance
12.3.3 Time-Frequency Representation of Power Quality Disturbance
12.3.4 Time-Scale Representation of Power Quality Disturbance
Bibliography
Appendix
Chapter 1: Generation Of Continuous-Time Signals
Answers to PreLab Questions
Answers to Objective Questions
Chapter 2: Sampling and Quantization of Signals
Answers to PreLab Questions
Answers to Objective Questions
Chapter 3: Generation and Operation on Discrete-Time Sequence
Answers to PreLab Questions
Answers to Objective Questions
Chapter 4: Discrete-Time Systems
Answers to PreLab Questions
Answers to Objective Questions
Chapter 5: Transforms
Answers to PreLab Questions
Answers to Objective Questions
Chapter 6: Filter Design Using Pole-Zero Placement Method
Answers to PreLab Questions
Answers to Objective Questions
Chapter 7: FIR Filter Design
Answers to PreLab Questions
Answers to Objective Questions
Chapter 8: Infinite Impulse Response Filter
Answers to PreLab Questions
Answers to Objective Questions
Chapter 9: Quantization Effect of Digital Filter Coefficients
Answers to PreLab Questions
Answer to Objective Questions
Chapter 10: Multirate Signal Processing
Answers to PreLab Questions
Answers to Objective Questions
Chapter 11: Adaptive Signal Processing
Answers to PreLab Questions
Answers to Objective Questions
Index