Introduction to Digital Signal Processing Using MATLAB

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1 Introduction to Digital Signal Processing Using MATLAB Second Edition Robert J. Schilling and Sandra L. Harris Clarkson University Potsdam, NY... CENGAGE l.earning: Australia Brazil Japan Korea Mexico Singapore Spain United Kingdom United States

2 Contents Margin Contents xvii PART I Signal and System Analysis Signal Processing Motivation Digital and Analog Processing Total Harmonie Distortion (THD) A Notch Filter Active Noise ContraI Video Aliasing Signals and Systems Signal Classification System Classification Sampling of Continuous-time Signals Sampling as Modulation Aliasing Reconstruction of Continuous-time Signals Reconstruction Formula Zero-order Hold Prefilters and Postfilters Anti-aliasing Filter Anti-imaging Filter 37 *1.6 DAC and ADC Circuits Digital-to-analog Converter (DAC) Analog-to-digital Converter (ADC) The FDSP Toolbox FDSP Driver Module Toolbox Functions GUI Modules GUI Software and Case Studies Chapter Summary 60 Sections marked with a contain more advanced or specialized material thatcan be skipped without loss of continuity. ix

3 x Contents 1.10 Problems Analysis and Design GUI Simulation MATLAB Computation 68 11I. 2 Discrete-time Systems in the Time Domain Motivation Home Mortgage Range Measurement with Radar Discrete-time Signals Signal Classification Common Signals Discrete-time Systems Difference Equations Zero-input Response Zero-stare Response Block Diagrams The Impulse Response FIR Systems IIR Systems Convolution Linear Convolution Circular Convolution Zero Padding Deconvolution Polynomial Arithmetic Correlation Linear Cross-correlation CircUlar Cross-correlation Stability in thetime Domain GUI Software and Case Studies Chapter Summary Problems Analysis and Design GUI Simulation MATLAB Computation I. 3 Discrete-time Systems in the Frequency Domain Motivation Satellite Attitude Control Modeling thevocal Tract Z-transform Pairs Region of Convergence Common Z-transform Pairs Z-transform Properties General Properties Causal Properties 162

4 Contents xi 3.4 InverseZ-transform Noneausal Signals Synthetie Division Partial Fraetions Residue Method Transfer Funetions The Transfer Funetion Zero-State Response Poles, Zeros, and Modes DC Gain Signal Flow Graphs Stability in the Frequeney Domain Input-output Representations BIBO Stability TheJuryTest Frequeney Response Frequeney Response Sinusoidal Inputs Periodie Inputs System Identifieation Least-squares Fit Persistently Exeiting Inputs GUI Software and Case Studies g_sysfreq: Discrete-time System Analysis in the Frequeney Domain Chapter Summary Problems Analysis and Design GLiI Simulation MATLAB Computation I 11 1Il. "... 4 Fourier Transforms and Spectral Analysis Motivation Fourier Series DC Wall Transformer Frequeney Response Discrete-time Fourier Transform (DTFT) DTFT Properties of the DTFT Discrete Fourier Transform (DFT) DFT Matrix Formulation Fourier Series and Discrete Speetra DFT Properties Fast Fourier Transform (FFT) Decimation in Time FFT FFT Computational Effort Alternative FFT Implementations 262

5 xii Contents 4.5 Fast Convolution and Correlation Fast Convolution 263 *4.5.2 Fast Block Convolution Fast Correlation White Noise Uniform White Noise Gaussian White Noise Auto-correlation Auto-correlation of White Noise Power Density Spectrum Extracting Periodic Signals frorn Noise Zero Padding and Spectral Resolution Frequency Response Using the DFT Zero Padding Spectral Resolution Spectrogram Data Windows Spectrogram Power Density Spectrum Estimation Bartlett's Method Welch's Method GUI Software and Case Studies Chapter Summary Problems Analysis and Design GUI Simulation MATLAB Computation 331 PART 11 Digital Filter Design 335 ".lt"" 5 Filter Design Specifications Motivation Filter Design Specifications Filter Realization Structures Frequency-selective Filters Linear Design Specifications Logarithmic Design Specifications (db) Linear-phase and Zero-phase Filters Linear Phase Zero-phase Filters Minimum-phase and Allpass Filters Minimum-phase Filters Allpass Filters Inverse Systems and Equalization Quadrature Filters Differentiator Hilbert Transformer Digital Oscillator 372

6 Contents xiii 5.6 Notch Filters and Resonators Notch Filters Resonators Narrowband Filters and Filter Banks Narrowband Filters Filter Banks Adaptive Filters GUI Software and Case Study g_filters: Evaluation of Digital Filter Characteristics Chapter Summary Problems Analysis and Design GUI Simulation MATLAB Computation ~ ~ 6 FIR Filter Design Motivation Numerical Differentiators Signal-to-noise Ratio Windowing Method Truncated Impulse Response Windowing Frequency-sampling Method Frequency Sampling Transition-band Optimization Least-squares Method Equiripple Filters Minimax Error Criterion Parks-McClellan Aigorithm Differentiators and Hilbert Transformers Differentiators Hilbert Transformers Quadrature Filters Generation of a Quadrature Pair Quadrature Filter Equalizer Design Filter Realization Structures Direct Forms Cascade Form Lattice Form 461 *6.9 Finite Word Length Effects Binary Number Representation Input Quantization Error Coefficient Quantization Error Roundoff Error, Overflow, and Scaling GUI Software and Case Study Chapter Summary 484

7 xiv Contents 6.12 Problems Analysis and Design GLII Simulation MATLAB Computation "'''' 7 UR Filter Design Motivation Tunable Plucked-string Filter Colored Noise Filter Design by Pole-zero Placement Resonator Notch Filter Comb Filters Filter Design Parameters C1assical Analog Filters Butterworth Filters Chebyshev-I Filters Chebyshev-II Filters Elliptic Filters Bilinear transformation Method Frequency Transformations Analog Frequency Transformations Digital Frequency Transformations Filter Realization Structures DirectForms Parallel Form Cascade Form 547 *7.8 Finite Word Length Effects Coefficient Quantization Error Roundoff Error, Overflow, and Scaling Limit Cycles GUI Sohware and Case Study Chapter Summary Problems Analysis and Design GUI Simulation MATLAB Computation PART 111 Advanced Signal Processing Multirate Signal Processing Motivation Narrowband Filter Banks Fractional Delay Systems Integer Sampling Rate Converters Sampling Rate Decimator Sampling Rate Interpolator 588

8 Contents xv 8.3 Rational Sampling Rate Converters Single-stage Converters Multistage Converters Multirate Filter Realization Structures Polyphase Decimator Polyphase Interpolator Narrowband Filters and Filter Banks Narrowband Filters Filter Banks A Two-channel QMF Bank Rate Converters in the Frequency Domain An Alias-free QNlF Bank Oversampling ADC Anti-aliasing Filters Sigma-delta ADC Oversampling DAC Anti-imaging Filters Passband Equalization GUI Software andcase Study Chapter Summary Problems Analysis and Design GUI Simulation MATLAB Computation "" 9 Adaptive Signal Processing Motivation System Identification Channel Equalization Signal Prediction Noise Cancellation Mean Square Error Adaptive Transversal Filters Cross-correlation Revisited Mean Square Error The Least Mean Square (LMS) Method Performance Analysis of LMS Method Step Size Convergence Rate Excess Mean Square Error Modified LMS Methods l'jormalized LMS Method Correlation LMS Method Leaky LMS Method Adaptive FIR Filter Design Pseudo-filters Linear-phase Pseudo-filters 681

9 xvi Contents 9.7 The Recursive Least-Squares (RLS) Method Performance Criterion Recursive Formulation Active Noise Control The Filtered-x LMS Method Secondary Path Identification Signal-synthesis Method Nonlinear System Identification Nonlinear Discrete-time Systems Grid Points Radial Basis Functions 70~ Adaptive RBF Networks GUI Software and Case Study Chapter Summary Problems Analysis and Design GUI Simulation MATLAB Computation 727 1II It «I... References and Further Reading Appendix 1 Transform Tables Fourier Series Fourier Transform Laplace Transform Z-transform Discrete-time Fourier Transform Discrete Fourier Transform (DFT) 745. Appendix 2 MathematicalIdentities Complex l\jumbers Euler's Identity Trigonometrie Identities Inequalities Uniform White Noise 749 «I... Appendix 3 FDSP Toolbox Functions Installation Driver Module: Cdsp Chapter GUI Modules FDSP Toolbox Functions 752 "... CI... Index 755

Digital Signal Processing

Digital Signal Processing Fourth Edition John G. Proakis Department of Electrical and Computer Engineering Northeastern University Boston, Massachusetts Dimitris G. Manolakis MIT Lincoln Laboratory Lexington,