Digital Signal Processing: Illustration Using Python

Preface....5 Motivation....5 Target Audience....6 Salient Features of the Book....6 Organization of the Book....7 Acknowledgments....9 Contents....10 About the Authors....15 Chapter 1: Generation of Continuous-Time Signals....17 1.1 Continuous-Time Signal....18 1.1.1 Continuous-Time Periodic Signal....19 1.1.2 Exponential Function....24 1.2 Non-stationary Signal....33 1.3 Non-sinusoidal Waveform....37 1.3.1 Square Waveform....37 1.3.2 Triangle and Sawtooth Waveform....38 1.3.3 Sinc Function....38 1.3.4 Pulse Signal....41 1.3.5 Gaussian Function....42 Bibliography....49 Chapter 2: Sampling and Quantization of Signals....50 2.1 Sampling of Signal....51 2.1.1 Violation of Sampling Theorem....54 2.1.2 Quantization of Signal....60 2.1.2.1 Mid-Tread Quantizer....61 2.1.3 Mid-Rise Quantizer....64 2.2 Non-uniform Quantization....70 2.3 Signal Reconstruction....74 2.3.1 Zero-Order Hold Interpolation....75 2.3.2 First-Order Hold Interpolation....77 2.3.3 Ideal or Sinc Interpolation....79 Bibliography....85 Chapter 3: Generation and Operation on Discrete-Time Sequence....86 3.1 Generation of Discrete-Time Signals....88 3.2 Mathematical Operation on Discrete-Time Signals....99 3.2.1 Amplitude Modification on DT Signal....99 3.2.1.1 Time Scaling Operation....106 3.2.1.2 Time Shifting Operation....108 3.2.1.3 Time Reversal Operation....110 3.3 Convolution....112 3.4 Correlation....126 Bibliography....137 Chapter 4: Discrete-Time Systems....138 4.1 Discrete-Time System....140 4.2 Representation of DT Systems....140 4.2.1 Difference Equation Representation of Discrete-Time Linear Time-Invariant System....140 4.2.2 State-Space Model of a Discrete-Time System....145 4.2.2.1 State-Space to Transfer Function....145 4.2.3 Impulse Response and Step Response of Discrete-Time System....149 4.2.4 Pole-Zero Plot of Discrete-Time System....154 4.3 Responses of Discrete-Time System....157 4.4 Different Representations and Response of Unit Delay Discrete-Time System....160 4.5 Properties of Discrete-Time System....164 4.5.1 Linearity Property....164 4.5.2 Time-Invariant and Time-Variant System....166 4.5.3 Causal and Non-causal System....168 4.5.4 Stability of Discrete-Time System....169 4.5.5 Invertibility of Discrete-Time System....173 Bibliography....180 Chapter 5: Transforms....181 5.1 Introduction to Transform....183 5.2 Z-Transform....183 5.2.1 Z-Transform of Standard Test Sequences....184 5.3 Inverse Z-Transform....187 5.4 Family of Fourier Series and Transforms....188 5.4.1 Continuous-Time Fourier Transform (CTFT)....189 5.4.2 Fourier Transform of Standard Test Signals....193 5.4.3 Discrete-Time Fourier Transform (DTFT)....205 5.4.4 Analysis of Discrete-Time LTI System Using DTFT....207 5.4.5 Discrete Fourier Transform....210 5.4.6 Properties of DFT....214 5.4.7 Limitations of Fourier Transform....218 5.5 Discrete Cosine Transform (DCT)....220 5.6 Short-Time Fourier Transform....224 5.6.1 Shortcoming of STFT....233 5.7 Continuous Wavelet Transform (CWT)....233 5.7.1 Continuous Wavelets Family....234 5.7.2 Drawback of CWT....235 5.8 Discrete Wavelet Transform....235 Bibliography....244 Chapter 6: Filter Design Using Pole-Zero Placement Method....245 6.1 First-Order IIR Filter....246 6.2 Moving Average filter....253 6.3 M-Point Exponentially Weighted Moving Average Filter (EWMA)....256 6.4 Digital Resonator....260 6.5 Notch Filter....262 6.6 All-Pass Filter....265 6.7 Comb Filter....269 6.7.1 Location of Poles and Zeros of Comb Filter....270 Bibliography....275 Chapter 7: FIR Filter Design....276 7.1 FIR Filter....277 7.2 Classification of FIR Filter....277 7.3 Design of FIR Filter....284 7.3.1 Steps in Window-Based FIR Filter Design....285 7.3.2 Window-Based FIR Lowpass Filter....286 7.3.3 Window-Based FIR Highpass Filter....289 7.3.4 Window-Based FIR Bandpass Filter....291 7.3.5 Window-Based FIR Band Reject Filter....293 7.3.6 Design of FIR Filter Using Built-In Function....295 7.3.7 Window Functions....301 7.4 Frequency Sampling-Based FIR Filter Design....304 7.5 Design of Optimal FIR filter....306 7.6 Applications of FIR Filter....307 Bibliography....315 Chapter 8: Infinite Impulse Response Filter....316 8.1 IIR Filter....317 8.2 Mapping Techniques in the Design of IIR Filter....319 8.2.1 Backward Difference Method....320 8.2.2 Impulse Invariant Technique....323 8.2.3 Bilinear Transformation Technique (BLT)....333 8.2.4 Matched Z-Transform Technique....336 8.3 Analog Frequency Transformation....339 8.4 Butterworth Filter....341 8.5 Chebyshev Filter....357 8.6 Chebyshev Type II IIR Filter....371 8.7 Elliptic Filter....375 Bibliography....389 Chapter 9: Quantization Effect of Digital Filter Coefficients....390 9.1 Number Representation....391 9.2 Fixed-Point Quantization....391 9.2.1 Fixed-Point Quantization by Rounding....392 9.2.2 Fixed-Point Quantization Using Two´s Complement Truncation....393 9.2.3 Fixed-Point Quantization Using Magnitude Truncation....394 9.3 Coefficient Quantization....396 9.4 Limit Cycle Oscillations....405 9.5 Cascade Form of a Higher Order Filters....410 Bibliography....414 Chapter 10: Multirate Signal Processing....416 10.1 Multirate Operators....418 10.1.1 Downsampling Operation....418 10.1.2 Upsampling Operation....422 10.2 Noble Identity....426 10.2.1 Noble Identity for Downsampling Operation....426 10.2.2 Noble Identity for Upsampling Operation....428 10.3 Polyphase Decomposition....430 10.4 Filter Bank....432 10.4.1 Two-Channel Filter Bank....433 10.4.2 Relationship Between Analysis and Synthesis Filters....434 10.4.3 Two-Channel Filter Bank Without Filters....437 10.4.4 Three-Channel Filter Bank Without Filters....439 10.5 Tree-Structured Filter Bank....441 10.6 Transmultiplexer....444 Bibliography....453 Chapter 11: Adaptive Signal Processing....455 11.1 Wiener Filter....456 11.1.1 Wiener Filter in Frequency Domain....459 11.2 Adaptive Filter....463 11.2.1 LMS Adaptive Filter....464 11.2.2 Normalized LMS Algorithm....469 11.2.3 Sign LMS Algorithm....471 11.3 RLS Algorithm....474 Bibliography....480 Chapter 12: Case Study....481 12.1 Case Study 1: Speech Recognition Using MFCC (Mel-Frequency Cepstral Coefficient)....481 12.1.1 Speaker Identification....482 12.1.2 Speaker Verification System....483 12.1.3 Mel-Frequency Cepstral Coefficient (MFCC) Feature....484 12.1.3.1 Pre-emphasis....484 12.1.3.2 Sampling and Windowing....484 12.1.3.3 Discrete Fourier Transform (DFT)....486 12.1.3.4 Mel-Frequency Bandpass Filter....488 12.1.3.5 Log Operation....490 12.1.3.6 Discrete Cosine Transform (DCT)....490 12.2 Case Study 2: QRS Detection in ECG Signal Using Pan-Tomkins Algorithm....491 12.2.1 ECG Signal Preprocessing....493 12.2.1.1 Bandpass filter....494 12.2.1.2 Derivative Process....495 12.2.1.3 Squaring Operation....495 12.2.2 Moving Window Integration....496 12.2.3 Fiducial Mark....496 12.2.4 Decision Rule Approach....498 12.3 Case Study 3: Power Quality Disturbance Detection....500 12.3.1 Generation of Power Quality Disturbance....501 12.3.2 Simulation of Power Quality Disturbance....503 12.3.3 Time-Frequency Representation of Power Quality Disturbance....504 12.3.4 Time-Scale Representation of Power Quality Disturbance....505 Bibliography....508 Appendix....509 Chapter 1: Generation Of Continuous-Time Signals....509 Answers to PreLab Questions....509 Answers to Objective Questions....511 Chapter 2: Sampling and Quantization of Signals....512 Answers to PreLab Questions....512 Answers to Objective Questions....513 Chapter 3: Generation and Operation on Discrete-Time Sequence....513 Answers to PreLab Questions....513 Answers to Objective Questions....515 Chapter 4: Discrete-Time Systems....515 Answers to PreLab Questions....515 Answers to Objective Questions....518 Chapter 5: Transforms....518 Answers to PreLab Questions....518 Answers to Objective Questions....520 Chapter 6: Filter Design Using Pole-Zero Placement Method....520 Answers to PreLab Questions....520 Answers to Objective Questions....521 Chapter 7: FIR Filter Design....521 Answers to PreLab Questions....521 Answers to Objective Questions....523 Chapter 8: Infinite Impulse Response Filter....523 Answers to PreLab Questions....523 Answers to Objective Questions....525 Chapter 9: Quantization Effect of Digital Filter Coefficients....525 Answers to PreLab Questions....525 Answer to Objective Questions....526 Chapter 10: Multirate Signal Processing....527 Answers to PreLab Questions....527 Answers to Objective Questions....529 Chapter 11: Adaptive Signal Processing....529 Answers to PreLab Questions....529 Answers to Objective Questions....530 Index....531