Handbook of Digital Signal Processing (eBook)

Front Cover 1
Handbook of Digital Signal Processing: Engineering Applications 4
Copyright Page 5
Table of Contents 6
Preface 12
Acronyms and Abbreviations 14
Notation 18
Chapter 1. Transforms and Transform Properties 24
I. Introduction 24
II. Review of Fourier Series 25
III. Discrete-Time Fourier Transform 29
IV. z-Transform 39
V. Laplace Transform 47
VI. Table of z-Transforms and Laplace Transforms 50
VII. Discrete Fourier Transform 50
VIII. Discrete-Time Random Sequences 64
IX. Correlation and Covariance Sequences 68
X. Power Spectral Density 73
XI. Summary 74
References 76
Chapter 2. Design and Implementation of Digital FIR Filters 78
I. Introduction 78
II. FIR Digital Filter Preliminaries 79
III. FIR Filter Design Based on Windowing 84
IV. Equiripple Approximations for FIR Filters 94
V. Maximally Flat Approximations for FIR Filters 113
VI. Linear Programming Approach for FIR Filter Designs 118
VII. Frequency Transformations in FIR Filters 123
VIII. Two-Dimensional Linear-Phase FIR Filter Design and Implementation 135
IX. Recent Techniques for Efficient FIR Filter Design 141
X. Other Useful Types of FIR Filters 159
XI. Summary 169
Appendix A. Design Charts for Digital FIR Differentiators and Hilbert Transformers 170
Appendix B. Program Listings for Linear-Phase FIR Filter Design 173
References 193
Chapter 3. Multirate FIR Filters for Interpolating and Desampling 196
I. Introduction 196
II. Characteristics of Bandwidth-Reducing FIR Filters 203
III. Data Rate Reduction (Desampling) by 1/M Filters 231
IV. Heterodyne Processing 246
V. Interpolating Filters 257
VI. Architectural Models for FIR Filters 268
VII. Summary 275
Appendix. Windows as Narrowband Filters 276
References 309
Chapter 4. IIR Digital Filters 312
I. Introduction 312
II. Preliminaries 313
III. Stability 314
IV. Digital Filter Realizations 318
V. Frequency Domain Design 323
VI. Analog Filter Design and Filter Types 329
VII. Frequency Transformations 354
VIII. Digital Filter Design Based on Analog Transfer Functions 355
IX. Spectral Transformations 366
X. Digital Filters Based on Continuous-Time Ladder Filters 367
XI. Summary 376
Appendix. IIR Digital Filter CAD Programs 378
References 378
Chapter 5. Low-Noise and Low-Sensitivity Digital Filters 382
I. Introduction 382
II. Binary Numbers—Representation and Quantization 384
III. Generation and Propagation of Roundoff Noise in Digital Filters 392
IV. Dynamic Range Constraints and Scaling 396
V. Signal-to-Roundoff-Noise Ratio in Simple IIR Filter Structures 401
VI. Low-Noise IIR Filter Sections Based on Error-Spectrum Shaping 410
VII. Signal-to-Noise Ratio in General Digital Filter Structures 418
VIII. Low-Noise Cascade-Form Digital Filter Implementation 419
IX. Noise Reduction in the Cascade Form by ESS 422
X. Low-Noise Designs via State-Space Optimization 425
XI. Parameter Quantization and Low-Sensitivity Digital Filters 435
XII. Low-Sensitivity Second-Order Sections 439
XIII. Wave Digital Filters 442
XIV. The Lossless Bounded Real Approach for the Design of Low-Sensitivity Filter Structures 457
XV. Structural Losslessness and Passivity 466
XVI. Low-Sensitivity All-Pass-Based Digital Filter Structures 467
XVII. Digital All-Pass Functions 476
XVIII. Orthogonal Digital Filters 481
XIX. Quantization Effects in FIR Digital Filters 483
XX. Low-Sensitive FIR Filters Based on Structural Passivity 488
XXI. Limit Cycles in IIR Digital Filters 492
References 498
Chapter 6. Fast Discrete Transforms 504
I. Introduction 504
II. Unitary Discrete Transforms 505
III. The Optimum Karhunen Loève Transform 506
IV. Sinusoidal Discrete Transforms 508
V. Nonsinusoidal Discrete Transforms 522
VI. Performance Criteria 533
VII. Computational Complexity and Summary 539
Appendix A. Fast Implementation of DCT via FFT 540
Appendix B. DCT Calculation Using an FFT 544
Appendix C. Walsh–Hadamard Computer Program 546
References 546
Chapter 7. Fast Fourier Transforms 550
I. Introduction 550
II. DFTs and DFT Representations 551
III. FFTs Derived from the MIR 555
IV. Radix-2 FFTs 576
V. Radix-3 and Radix-6 FFTs 581
VI. Radix-4 FFTs 587
VII. Small-N DFTs 588
VIII. FFTs Derived from the Ruritanian Correspondence (RC) 590
IX. FFTs Derived from the Chinese Remainder Theorem 594
X. Good's FFT 596
XI. Kronecker Product Representation of Good's FFT 597
XII. Polynomial Transforms 602
XIII. Comparison of Algorithms 603
XIV. FFT Word Lengths 610
XV. Summary 618
Appendix A. Small-N DFT Algorithms 619
Appendix B. FFT Computer Programs 623
Appendix C. Radix-2 FFT Program 625
Appendix D. Prime Factor Algorithm (PFA) 628
Appendix E. Highly Efficient PFA Assembly Language Computer Program 644
References 653
Chapter 8. Time Domain Signal Processing with the DFT 656
I. Introduction 656
II. The DFT as a Bank of Narrowband Filters 662
III. Fast Convolution and Correlation 689
IV. The DFT as an Interpolator and Signal Generator 706
V. Summary 721
References 721
Chapter 9. Spectral Analysis 724
I. Introduction 724
II. Rational Spectral Models 725
III. Rational Modeling: Exact Autocorrelation Knowledge 730
IV. Overdetermined Equation Modeling Approach 737
V. Detection of Multiple Sinusoids in White Noise 739
VI. MA Modeling: Time Series Observations 744
VII. AR Modeling: Time Series Observations 746
VIII. ARMA Modeling: Time Series Observations 747
IX. ARMA Modeling: A Singular Value Decomposition Approach 749
X. Numerical Examples 754
XI. Conclusions 762
References 762
Chapter 10. Deconvoliition 764
I. Introduction 764
II. Deconvolution and LTI Systems with No Measurement Noise 769
III. Deconvolution and the Identification of DTLTI Systems with Measurement Noise 783
IV. Fast Algorithms for Deconvolution Problems 789
V. Some Practical Applications of Deconvolution 800
VI. Summary 807
Appendix A. References for Obtaining Computational Algorithms 808
Appendix B. Implementing the Levinson or Toeplitz Recursion 809
Appendix C. Implementing the Lattice Form of the Levinson Recursion 810
References 810
Chapter 11. Time Delay Estimation 812
I. Introduction 812
II. Time Delay Estimation for Active Sensors 816
III. Time Delay Estimation for Passive Sensors 841
IV. Cross-Correlation and Its Relationship to the Time Delay Estimation Problem 856
V. The Implementation of Some Time Delay Estimation Algorithms Using the Fast Fourier Transform (FFT) 860
VI. Algorithm Performance 867
VII. Summary 876
References 876
Chapter 12. Adaptive Filtering 880
I. Introduction 880
II. Some Matrix Operations 881
III. A Class of Optimal Filters 883
IV. Least-Mean-Squares (LMS) Algorithm 889
V. LMS Lattice Algorithms 905
VI. Concluding Remarks 911
Appendix. Four FORTRAN-77 Programs 912
References 919
Chapter 13. Recursive Estimation 922
I. Introduction 922
II. Least Squares Estimation 923
III. Linear Minimum Mean Square Estimation 931
IV. Discrete Kalman Filtering Examples 938
V. Extensions 945
VI. Some Computational Considerations 952
VII. Summary 961
References 961
Chapter 14. Mechanization of Digital Signal Processors 964
I. Introduction 964
II. Digital Machine Fundamentals 965
III. The Essence of Digital Signal Processing 970
IV. Number Representations 970
V. Hardware Components 973
VI. Microprogramming 982
VII. Keeping Things in Perspective 986
VIII. Distributed Arithmetic 987
IX. Summary 995
References 995
Addendum to Chapter 3. Window Generation Computer Program 998
Index 1010

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