دانلود کتاب Digital Filter Design and Realization

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Front Cover Half Title Page RIVER PUBLISHERS SERIES IN SIGNAL, IMAGE AND SPEECH PROCESSING Title Page - Digital Filter Design and Realization Copyright Page Contents Preface List of Figures List of Tables List of Abbreviations Chapter 1 - Introduction 1.1 Preview 1.2 Terminology for Signal Analysis and Typical Signals 1.2.1 Terminology for Signal Analysis 1.2.2 Examples of Typical Signals 1.3 Digital Signal Processing 1.3.1 General Framework for Digital Signal Processing 1.3.2 Advantages of Digital Signal Processing 1.3.3 Disadvantages of Digital Signal Processing 1.4 Analysis of Analog Signals 1.4.1 The Fourier Series Expansion of Periodic Signals 1.4.2 The Fourier Transform 1.4.3 The Laplace Transform 1.5 Analysis of Discrete-Time Signals 1.5.1 Sampling an Analog Signal 1.5.2 The Discrete-Time Fourier Transform 1.5.3 The Discrete Fourier Transform (DFT) 1.5.4 The z-Transform 1.6 Sampling of Continuous-Time Sinusoidal Signals 1.7 Aliasing 1.8 Sampling Theorem 1.9 Recovery of an Analog Signal 1.10 Summary References Chapter 2 - Discrete-Time Systems and z-Transformation 2.1 Preview 2.2 Discrete-Time Signals 2.3 z-Transform of Basic Sequences 2.3.1 Fundamental Transforms 2.3.2 Properties of z-Transform 2.4 Inversion of z-Transforms 2.4.1 Partial Fraction Expansion 2.4.2 Power Series Expansion 2.4.3 Contour Integration 2.5 Parseval’s Theorem 2.6 Discrete-Time Systems 2.7 Difference Equations 2.8 State-Space Descriptions 2.8.1 Realization 1 2.8.2 Realization 2 2.9 Frequency Transfer Functions 2.9.1 Linear Time-Invariant Causal Systems 2.9.2 Rational Transfer Functions 2.9.3 All-Pass Digital Filters 2.9.4 Notch Digital Filters 2.9.5 Doubly Complementary Digital Filters 2.10 Summary References Chapter 3 - Stability and Coefficient Sensitivity 3.1 Preview 3.2 Stability 3.2.1 Definition 3.2.2 Stability in Terms of Poles 3.2.3 Schur-Cohn Criterion 3.2.4 Schur-Cohn-Fujiwara Criterion 3.2.5 Jury-Marden Criterion 3.2.6 Stability Triangle of Second-Order Polynomials 3.2.7 Lyapunov Criterion 3.3 Coefficient Sensitivity 3.4 Summary References Chapter 4 - State-Space Models 4.1 Preview 4.2 Controllability and Observability 4.3 Transfer Function 4.3.1 Impulse Response 4.3.2 Faddeev’s Formula 4.3.3 Cayley-Hamilton’s Theorem 4.4 Equivalent Systems 4.4.1 Equivalent Transformation 4.4.2 Canonical Forms 4.4.3 Balanced, Input-Normal, and Output-Normal State-Space Models 4.5 Kalman’s Canonical Structure Theorem 4.6 Hankel Matrix and Realization 4.6.1 Minimal Realization 4.6.2 Minimal Partial Realization 4.6.3 Balanced Realization 4.7 Discrete-Time Lossless Bounded-Real Lemma 4.8 Summary References Chapter 5 - FIR Digital Filter Design 5.1 Preview 5.2 Filter Classification 5.3 Linear-phase Filters 5.3.1 Frequency Transfer Function 5.3.2 Symmetric Impulse Responses 5.3.3 Antisymmetric Impulse Responses 5.4 Design Using Window Function 5.4.1 Fourier Series Expansion 5.4.2 Window Functions 5.4.3 Frequency Transformation 5.5 Least-Squares Design 5.5.1 Quadratic-Measure Minimization 5.5.2 Eigenfilter Method 5.6 Analytical Approach 5.6.1 General FIR Filter Design 5.6.2 Linear-Phase FIR Filter Design 5.7 Chebyshev Approximation 5.7.1 The Parks-McClellan Algorithm 5.7.2 Alternation Theorem 5.8 Cascaded Lattice Realization of FIR Digital Filters 5.9 Numerical Experiments 5.9.1 Least-Squares Design 5.9.1.1 Quadratic measure minimization 5.9.1.2 Eigenfilter method 5.9.2 Analytical Approach 5.9.2.1 General FIR filter design 5.9.2.2 Linear-Phase FIR filter design 5.9.3 Chebyshev Approximation 5.9.4 Comparison of Algorithms’ Performances 5.10 Summary References Chapter 6 - Design Methods Using Analog Filter Theory 6.1 Preview 6.2 Design Methods Using Analog Filter Theory 6.2.1 Lowpass Analog-Filter Approximations 6.2.1.1 Butterworth approximation 6.2.1.2 Chebyshev approximation 6.2.1.3 Inverse-Chebyshev approximation 6.2.1.4 Elliptic approximation 6.2.2 Other Analog-Filter Approximations by Transformations 6.2.2.1 Lowpass-to-lowpass transformation 6.2.2.2 Lowpass-to-highpass transformation 6.2.2.3 Lowpass-to-bandpass transformation 6.2.2.4 Lowpass-to-bandstop transformation 6.2.3 Design Methods Based on Analog Filter Theory 6.2.3.1 Invariant impulse-response method 6.2.3.2 Bilinear-transformation method 6.3 Summary References Chapter 7 - Design Methods in the Frequency Domain 7.1 Preview 7.2 Design Methods in the Frequency Domain 7.2.1 Minimum Mean Squared Error Design 7.2.2 An Equiripple Design by Linear Programming 7.2.3 Weighted Least-Squares Design with Stability Constraints 7.2.4 Minimax Design with Stability Constraints 7.3 Design of All-Pass Digital Filters 7.3.1 Design of All-Pass Filters Based on Frequency Response Error 7.3.2 Design of All-Pass Filters Based on Phase Characteristic Error 7.3.3 A Numerical Example 7.4 Summary References Chapter 8 - Design Methods in the Time Domain 8.1 Preview 8.2 Design Based on Extended Pade’s Approximation 8.2.1 A Direct Procedure 8.2.2 A Modified Procedure 8.3 Design Using Second-Order Information 8.3.1 A Filter Design Method 8.3.2 Stability 8.3.3 An Efficient Algorithm for Solving (8.35) 8.4 Least-Squares Design 8.5 Design Using State-Space Models 8.5.1 Balanced Model Reduction 8.5.2 Stability and Minimality 8.6 Numerical Experiments 8.6.1 Design Based on Extended Pade’s Approximation 8.6.2 Design Using Second-Order Information 8.6.3 Least-Squares Design 8.6.4 Design Using State-Space Model (Balanced Model Reduction) 8.6.5 Comparison of Algorithms’ Performances 8.7 Summary References Chapter 9 - Design of Interpolated and FRM FIR Digital Filters 9.1 Preview 9.2 Basics of IFIR and FRM Filters and CCP 9.2.1 Interpolated FIR Filters 9.2.2 Frequency-Response-Masking Filters 9.2.3 Convex-Concave Procedure (CCP) 9.3 Minimax Design of IFIR Filters 9.3.1 Problem Formulation 9.3.2 Convexification of (9.10) Using CCP 9.3.3 Remarks on Convexification in (9.13)–(9.14) 9.4 Minimax Design of FRM Filters 9.4.1 The Design Problem 9.4.2 A CCP Approach to Solving (9.23) 9.5 FRM Filters with Reduced Complexity 9.5.1 Design Phase 1 9.5.2 Design Phase 2 9.6 Design Examples 9.6.1 Design and Evaluation Settings 9.6.2 Design of IFIR Filters 9.6.3 Design of FRM Filters 9.6.4 Comparisons with Conventional FIR Filters 9.7 Summary References Chapter 10 - Design of a Class of Composite Digital Filters 10.1 Preview 10.2 Composite Filters and Problem Formulation 10.2.1 Composite Filters 10.2.2 Problem Formulation 10.3 Design Method 10.3.1 Design Strategy 10.3.2 Solving (10.7) with y Fixed to y = yk 10.3.3 Updating y with x Fixed to x = xk 10.3.4 Summary of the Algorithm 10.4 Design Example and Comparisons 10.5 Summary References Chapter 11 - FiniteWord Length Effects 11.1 Preview 11.2 Fixed-Point Arithmetic 11.3 Floating-Point Arithmetic 11.4 Limit Cycles—Overflow Oscillations 11.5 Scaling Fixed-Point Digital Filters to Prevent Overflow 11.6 Roundoff Noise 11.7 Coefficient Sensitivity 11.8 State-Space Descriptions with FiniteWord Length 11.9 Limit Cycle-Free Realization 11.10 Summary References Chapter 12 - l2-Sensitivity Analysis and Minimization 12.1 Preview 12.2 l2-Sensitivity Analysis 12.3 Realization with Minimal l2-Sensitivity 12.4 l2-Sensitivity Minimization Subject to l2-Scaling Constraints Using Quasi-Newton Algorithm 12.4.1 l2-Scaling and Problem Formulation 12.4.2 Minimization of (12.18) Subject to l2-Scaling Constraints — Using Quasi-Newton Algorithm 12.4.3 Gradient of J(x) 12.5 l2-Sensitivity Minimization Subject to l2-Scaling Constraints Using Lagrange Function 12.5.1 Minimization of (12.19) Subject to l2-Scaling Constraints — Using Lagrange Function 12.5.2 Derivation of Nonsingular T from P to Satisfy l2-Scaling Constraints 12.6 Numerical Experiments 12.6.1 Filter Description and Initial l2-Sensitivity 12.6.2 l2-Sensitivity Minimization 12.6.3 l2-Sensitivity Minimization Subject to l2-Scaling Constraints Using Quasi-Newton Algorithm 12.6.4 l2-Sensitivity Minimization Subject to l2-Scaling Constraints Using Lagrange Function 12.7 Summary References Chapter 13 - Pole and Zero Sensitivity Analysis and Minimization 13.1 Preview 13.2 Pole and Zero Sensitivity Analysis 13.3 Realization with Minimal Pole and Zero Sensitivity 13.3.1 Weighted Pole and Zero Sensitivity Minimization WithoutImposing l2-Scaling Constraints 13.3.2 Zero Sensitivity Minimization Subject to Minimal Pole Sensitivity 13.4 Pole Zero Sensitivity Minimization Subject to l2-Scaling Constraints Using Lagrange Function 13.4.1 l2-Scaling Constraints and Problem Formulation 13.4.2 Minimization of (13.37) Subject to l2-Scaling Constraints — Using Lagrange Function 13.4.3 Derivation of Nonsingular T from P to Satisfyl2-Scaling Constraints 13.5 Pole and Zero Sensitivity Minimization Subject to l2-Scaling Constraints Using Quasi-Newton Algorithm 13.5.1 l2-Scaling and Problem Formulation 13.5.2 Minimization of (13.68) Subject to l2-Scaling Constraints — Using Quasi-Newton Algorithm 13.5.3 Gradient of J(x) 13.6 Numerical Experiments 13.6.1 Filter Description and Initial Pole and Zero Sensitivity 13.6.2 Weighted Pole and Zero Sensitivity Minimization Without Imposing l2-Scaling Constraints 13.6.3 Weighted Pole and Zero Sensitivity Minimization Subject to l2-Scaling Constraints Using Lagrange Function 13.6.4 Weighted Pole and Zero Sensitivity Minimization Subject to l2-Scaling Constraints Using Quasi-Newton Algorithm 13.7 Summary References Chapter 14 - Error Spectrum Shaping 14.1 Preview 14.2 IIR Digital Filters with High-Order Error Feedback 14.2.1 Nth-Order Optimal Error Feedback 14.2.2 Computation of Autocorrelation Coefficients 14.2.3 Error Feedback with Symmetric or Antisymmetric Coefficients 14.3 State-Space Filter with High-Order Error Feedback 14.3.1 Nth-Order Optimal Error Feedback 14.3.2 Computation of Qi for i = 0, 1, · · · ,N − 1 14.3.3 Error Feedback with Symmetric orAntisymmetric Matrices 14.4 Numerical Experiments 14.4.1 Example 1 : An IIR Digital Filter 14.4.2 Example 2 : A State-Space Digital Filter 14.5 Summary References Chapter 15 - Roundoff Noise Analysis and Minimization 15.1 Preview 15.2 Filters Quantized after Multiplications 15.2.1 Roundoff Noise Analysis and Problem Formulation 15.2.2 Roundoff Noise Minimization Subject to l2-Scaling Constraints 15.3 Filters Quantized before Multiplications 15.3.1 State-Space Model with High-Order Error Feedback 15.3.2 Formula for Noise Gain 15.3.3 Problem Formulation 15.3.4 Joint Optimization of Error Feedback and Realization 15.3.4.1 The Use of Quasi-Newton Algorithm 15.3.4.2 Gradient of J(x) 15.3.5 Analytical Method for Separate Optimization 15.4 Numerical Experiments 15.4.1 Filter Description and Initial Roundoff Noise 15.4.2 The Use of Analytical Method in Section 15.2.2 15.4.3 The Use of Iterative Method in Section 15.3.4 15.5 Summary References Chapter 16 - Generalized Transposed Direct-Form II Realization 16.1 Preview 16.2 Structural Transformation 16.3 Equivalent State-Space Realization 16.3.1 State-Space Realization I 16.3.2 State-Space Realization II 16.3.3 Choice of {Δi} Satisfying l2-Scaling Constraints 16.4 Analysis of Roundoff Noise 16.4.1 Roundoff Noise of ρ-Operator Transposed Direct-Form II Structure 16.4.2 Roundoff Noise of Equivalent State-Space Realization 16.5 Analysis of l2-Sensitivity 16.5.1 l2-Sensitivity of ρ-Operator Transposed Direct-Form II Structure 16.5.2 l2-Sensitivity of Equivalent State-Space Realization 16.6 Filter Synthesis 16.6.1 Computation of Roundoff Noise and l2-Sensitivity 16.6.2 Choice of Parameters {γi| i = 1, 2, · · · , n} 16.6.3 Search of Optimal Vector γ = [γ1, γ2, · · · , γn]T 16.7 Numerical Experiments 16.8 Summary References Chapter 17 - Block-State Realization of IIR Digital Filters 17.1 Preview 17.2 Block-State Realization 17.3 Roundoff Noise Analysis and Minimization 17.3.1 Roundoff Noise Analysis 17.3.2 Roundoff Noise Minimization Subject to l2-Scaling Constraints 17.4 l2-Sensitivity Analysis and Minimization 17.4.1 l2-Sensitivity Analysis 17.4.2 l2-Sensitivity Minimization Subject to l2-Scaling Constraints 17.4.2.1 Method 1: using a Lagrange function 17.4.2.2 Method 2: using a Quasi-Newton algorithm 17.4.3 l2-Sensitivity Minimization Without Imposing l2-Scaling Constraints 17.4.4 Numerical Experiments 17.5 Summary References Index About the Authors Back Cover