Digital Signal Processing: Principles, Algorithms and Applications

Digital Signal Processing: Principles, Algorithms & Applications (3rd Ed.)......Page 1
Copyright......Page 3
Contents......Page 4
Preface......Page 14
Ch1 Introduction......Page 18
1.1 Signals, Systems & Signal Processing......Page 19
1.1.1 Basic Elements of DSP System......Page 21
1.1.2 Advantages of Digital over Analog Signal
Processing......Page 22
1.2 Classification of Signals......Page 23
1.2.1 Multichannel & Multidimensional Signals......Page 24
1.2.2 Continuous-Time vs Discrete-Time Signals......Page 25
1.2.3 Continuous-Valued vs Discrete-Valued Signals......Page 27
1.2.4 Deterministic vs Random Signals......Page 28
1.3.1 Continuous-Time Sinusoidal Signals......Page 31
1.3.2 Discrete-Time Sinusoidat Signals......Page 33
1.3.3 Harmonically Related Complex Exponentiais......Page 36
1.4 Analog-to-Digital & Digital-to-Analog Conversion......Page 38
1.4.1 Sampling of Analog Signals......Page 40
1.4.2 Sampling Theorem......Page 46
1.4.3 Quantization of Continuous-Amplitude Signals......Page 50
1.4.4 Quantization of Sinusoidal Signals......Page 53
1.4.6 Digital-to-Analog Conversion......Page 55
1.5 Summary & References......Page 56
Problems......Page 57
2.1 Discrete-Time Signals......Page 60
2.1.1 Some Elementary Discrete-Time Signals......Page 62
2.1.2 Classification of Discrete-Time Signals......Page 64
2.1.3 Simple Manipulations of Discrete-Time Signals......Page 69
2.2.1 Input-Output Description of Systems......Page 73
2.2.2 Block Diagram Representation of Discrete-Tlme
Systems......Page 76
2.2.3 Classification of Discrete-Time Systems......Page 79
2.2.4 Interconnection of Discrete-Time Systems......Page 87
2.3.1 Techniques for Analysis of Linear Systems......Page 89
2.3.2 Resolution of Discrete-Time Signal into Impulses......Page 91
2.3.3 Response of LTI Systems to Arbitrary Inputs: Convolution Sum......Page 92
2.3.4 Properties of Convolution & Interconnection of LTI Systems......Page 99
2.3.5 Causal Linear Time-Invariant Systems......Page 103
2.3.6 Stability of Linear Time-invariant Systems......Page 104
2.3.7 Systems with Finite-Duration & Infinite-Duration Impulse Response......Page 107
2.4 Discrete-Time Systems described by Difference Equations......Page 108
2.4.1 Recursive & Nonrecursive Discrete-Time Systems......Page 109
2.4.2 Linear Time-Invariant Systems characterized by Constant-Coefficient Difference Equation......Page 112
2.4.3 Solution of Linear Constant-Coefficient Difference Equations......Page 117
2.4.4 Impulse Response of Linear Time-Invariant Recursive System......Page 125
2.5.1 Structures for Realization of Linear Time-Invariant Systems......Page 128
2.5.2 Recursive & Nonrecursive Realizations of FIR Systems......Page 133
2.6 Correlation of Discrete-Time Signals......Page 135
2.6.1 Crosscorrelation & Autocorretation Sequences......Page 137
2.6.2 Properties of Autocorrelation & Crosscorrelation Sequences......Page 139
2.6.3 Correlation of Periodic Sequences......Page 141
2.6.4 Computation of Correlation Sequences......Page 147
2.6.5 Input-Output Correlation Sequences......Page 148
2.7 Summary & References......Page 151
Problems......Page 152
3.1 z-Transform......Page 168
3.1.1 Direct z-Transform......Page 169
3.1.2 Inverse z-Transform......Page 177
3.2 Properties of z-Transform......Page 178
3.3.1 Poles & Zeros......Page 189
3.3.2 Pole Location & Time-Domain Behavior for Causal Signals......Page 195
3.3.3 System Function of Linear Tirne-Invariant System......Page 198
3.4.1 Inverse z-Transform by Contour Integration......Page 201
3.4.2 Inverse z-Transform by Power Series Expansion......Page 203
3.4.3 Inverse z-Transform by Partial-Fraction Expansion......Page 205
3.4.4 Decomposition of Rational z-Transforms......Page 212
3.5.1 Definition & Properties......Page 214
3.5.2 Solution of Difference Equations......Page 218
3.6.1 Response of Systems with Rational System
Functions......Page 220
3.6.2 Response of Pole-Zero Systems with Nonzero
Initial Conditions......Page 221
3.6.3 Transient & Steady-State Responses......Page 223
3.6.4 Causality & Stability......Page 225
3.6.5 Pole-Zero Cancellations......Page 227
3.6.6 Multiple-Order Poles & Stability......Page 228
3.6.7 Schur-Cohn Stability Test......Page 230
3.6.8 Stability of Second-Order Systems......Page 232
3.7 Summary & References......Page 236
Problems......Page 237
4.1 Frequency Analysis of Continuous-Time Signals......Page 247
4.1.1 Fourier Series for Continuous-Time Periodic Signals......Page 249
4.1.2 Power Density Spectrum of Periodic Signals......Page 252
4.1.3 Fourier Transform for Continuous-Time Aperiodic Signals......Page 257
4.1.4 Energy Density Spectrum of Aperiodic Signals......Page 260
4.2.1 Fourier Series for Discrete-Time Periodic Signals......Page 264
4.2.2 Power Density Spectrum of Periodic Signals......Page 267
4.2.3 Fourier Transform of Discrete-Time Aperiodic Signals......Page 270
4.2.4 Convergence of Fourier Transform......Page 273
4.2.5 Energy Density Spectrum of Aperiodic Signals......Page 277
4.2.6 Relationship of Fourier Transform to z-Transform......Page 281
4.2.7 Cepstrum......Page 282
4.2.8 Fourier Transform of Signals with Poles on Unit Circle......Page 284
4.2.9 Sampling Theorem Revisited......Page 286
4.2.10 Frequency-Domain Classification of Signals: Concept of Bandwidth......Page 296
4.2.12 Physical & Mathematical Dualities......Page 299
4.3 Properties of Fourier Transform for Discrete-Time Signals......Page 303
4.3.1 Symmetry Properties of Fourier Transform......Page 304
4.3.2 Fourier Transform Theorems & Properties......Page 311
4.4 Frequency-Domain Characteristics of LTI Systems......Page 322
4.4.1 Response to Complex Exponential & Sinusoidal Signals: Frequency Response Function......Page 323
4.4.2 Steady-State & Transient Response to Sinusoidal Input Signals......Page 331
4.4.3 Steady-State Response to Periodic Input Signals......Page 332
4.4.4 Response to Aperiodic Input Signals......Page 333
4.4.5 Relationships between System Function & Frequency Response Function......Page 336
4.4.6 Computation of Frequency Response Function......Page 338
4.4.7 Input-Output Correlation Functions & Spectra......Page 342
4.4.8 Correlation Functions & Power Spectra for Random Input Signals......Page 344
4.5 LTI Systems as Frequency-Selective Filters......Page 347
4.5.1 Ideal Filter Characteristics......Page 348
4.5.2 Lowpass, Highpass & Bandpass Filters......Page 350
4.5.3 Digital Resonators......Page 357
4.5.4 Notch Filters......Page 360
4.5.5 Comb Filters......Page 362
4.5.6 All-Pass Filters......Page 367
4.5.7 Digital Sinusoidal Oscillators......Page 369
4.6 Inverse Systems & Deconvolution......Page 372
4.6.1 lnvertibility of LTI Systems......Page 373
4.6.2 Minimum-Phase, Maximum-Phase & Mixed-Phase Systems......Page 376
4.6.3 System Identification & Deconvolution......Page 380
4.6.4 Homomorphic Deconvolution......Page 382
4.7 Summary & References......Page 384
Problems......Page 385
5.1.1 Frequency-Domain Sampling & Reconstruction of Discrete-Time Signals......Page 411
5.1.2 Discrete Fourier Transform (DFT)......Page 416
5.1.3 DFT as Linear Transformation......Page 420
5.1.4 Relationship of DFT to other Transforms......Page 424
5.2 Properties of DFT......Page 426
5.2.1 Periodicity, Linearity & Symmetry Properties......Page 427
5.2.2 Multiplication of 2 DFTs & Circular Convolution......Page 432
5.2.3 Additional DFT Properties......Page 438
5.3 Linear Filtering Methods based on DFT......Page 442
5.3.1 Use of DFT in Linear Filtering......Page 443
5.3.2 Filtering of Long Data Sequences......Page 447
5.4 Frequency Analysis of Signals using DFT......Page 450
Problems......Page 457
6.1 Efnclent Computation of DFT: FFT Algorithms......Page 465
6.1.1 Direct Computation of DFT......Page 466
6.1.2 Divide-&-Conquer Approach to Computation of DFT......Page 467
6.1.3 Radix-2 FFT Algorithms......Page 473
6.1.4 Radix-4 FFT Algorithms......Page 482
6.1.5 Split-Radix FFT Algorithms......Page 487
6.1.6 Implementation of FFT Algorithms......Page 490
6.2.1 Efficient Computation of DTT of 2 Real Sequences......Page 492
6.2.2 Efficient Computation of DFT of 2N-Point Real Sequence......Page 493
6.2.3 Use of FFT Algorithm in Linear Filtering & Correlation......Page 494
6.3 Linear Filtering Approach to Computation of DFT......Page 496
6.3.1 Goertzel Algorithm......Page 497
6.3.2 Chirp-z Transform Algorithm......Page 499
6.4 Quantization Effects in Computation of DFT......Page 503
6.4.1 Quantization Errors in Direct Computation of DFT......Page 504
6.4.2 Quantization Errors in FFT Algorithms......Page 506
6.5 Summary & References......Page 510
Problems......Page 511
7.1 Structures for Realization Of Discrete-Time Systems......Page 517
7.2 Structures for FIR Systems......Page 519
7.2.1 Direct-Form Structure......Page 520
7.2.2 Cascade-Form Structures......Page 521
7.2.3 Frequency-Sampling Structures......Page 523
7.2.4 Lattice Structure......Page 528
7.3.1 Direct-Form Structures......Page 536
7.3.2 Signal Flow Graphs & Transposed Structures......Page 538
7.3.3 Cascade-Form Structures......Page 543
7.3.4 Parallel-Form Structures......Page 546
7.3.5 Lattice & Lattice-Ladder Structures for IIR Systems......Page 548
7.4 State-Space System Analysis & Structures......Page 556
7.4.1 State-Space Descriptions of Systems characterized by Difference Equations......Page 557
7.4.2 Solution of State-Space Equations......Page 560
7.4.3 Relationships between Input-Output & State-Space Descriptions......Page 562
7.4.4 State-Space Analysis in z-Domain......Page 567
7.4.5 Additional State-Space Structures......Page 571
7.5 Representation of Numbers......Page 573
7.5.1 Fixed-Point Representation of Numbers......Page 574
7.5.2 Binary Floating-Point Representation of Numbers......Page 578
7.5.3 Errors Resulting from Rounding & Truncation......Page 581
7.6.1 Analysis of Sensitivity to Quantization of Filter
Coefficients......Page 586
7.6.2 Quantization of Coefficients in FIR Filters......Page 595
7.7 Round-Off Effects in Digital Filters......Page 599
7.7.1 Limit-Cycle Oscillations in Recursive Systems......Page 600
7.7.2 Scaling to Prevent Overflow......Page 605
7.7.3 Statistical Characterization of Quantization Effects
in Fixed-Point Realizations of Digital Filters......Page 607
7.8 Summary & References......Page 615
Problems......Page 617
8.1 General Considerations......Page 631
8.1.1 Causality & its Implications......Page 632
8.1.2 Characteristics of Practical Frequency-Selective Filters......Page 636
8.2.1 Symmetric & Antisymmetric FIR Filters......Page 637
8.2.2 Design of Linear-Phase FIR Filters using Windows......Page 640
8.2.3 Design of Linear-Phase FIR Filters by Frequency-Sampling Method......Page 647
8.2.4 Design of Optimum Equiripple Linear-Phase FIR
Filters......Page 654
8.2.5 Design of FIR Differentiators......Page 669
8.2.6 Design of Hilbert Transformers......Page 674
8.2.7 Comparison of Design Methods for Linear-Phase
FIR Filters......Page 679
8.3 Design of IIR Fllters from Analog Filters......Page 683
8.3.1 IIR Filter Design by Approximation of Derivatives......Page 684
8.3.2 IIR Filter Design by Impulse lnvariance......Page 688
8.3.3 IIR Filter Design by Bilinear Transformation......Page 693
8.3.5 Characteristics of Commonly Used Analog Filters......Page 698
8.4 Frequency Transformations......Page 709
8.4.1 Frequency Transformations in Analog Domain......Page 710
8.4.2 Frequency Transformations in Digital Domain......Page 715
8.5.1 Pade Approximation Method......Page 718
8.5.2 Least-Squares Design Methods......Page 723
8.5.3 FIR Least-Squares Inverse (Wiener) Filters......Page 728
8.5.4 Design of IIR Filters In Frequency Domain......Page 736
8.6 Summary & References......Page 741
Problems......Page 743
9.1.1 Representation of Bandpass Signals......Page 755
9.1.2 Sampling of Bandpass Signals......Page 759
9.1.3 Discrete-Time Processing of Continuous-Time Signals......Page 763
9.2.1 Sample-and-Hold......Page 765
9.2.2 Quantization & Coding......Page 767
9.2.3 Analysis of Quantization Errors......Page 770
9.2.4 Oversampling A/D Converters......Page 773
9.3 Digital-to-Analog Conversion......Page 780
9.3.1 Sample & Hold......Page 782
9.3.2 First-Order Hold......Page 785
9.3.3 Linear Interpolation with Delay......Page 788
9.4 Summary & References......Page 791
Problems......Page 792
Ch10 Multirate Digital Signal Processing......Page 799
10.1 Introduction......Page 800
10.2 Decimation by Factor D......Page 801
10.3 Interpolation by Factor I......Page 804
10.4 Sampling Rate Conversion by Rational Factor 1/D......Page 807
10.5 Filter Design & Implementation for Sampling-Rate Conversion......Page 809
10.5.1 Direct-Form FIR Filter Structures......Page 810
10.5.2 Polyphase Filter Structures......Page 811
10.5.3 Time-Variant Filter Structures......Page 817
10.6 Multistage Implementation of Sampling-Rate Converslon......Page 823
10.7 Sampling-Rate Conversion of Bandpass Signals......Page 827
10.7.1 Decimation & Interpolation by Frequency Conversion......Page 829
10.7.2 Modulation-Free Method for Decimation & Interpolation......Page 831
10.8 Sampling-Rate Conversion by Arbitrary Factor......Page 832
10.8.1 1st-Order Approximation......Page 833
10.8.2 2nd-Order Approximation (Linear Interpolation)......Page 836
10.9.1 Design of Phase Shifters......Page 838
10.9.2 Interfacing of Digital Systems with Different
Sampling Rates......Page 840
10.9.3 Implementation of Narrowband Lowpass Filters......Page 841
10.9.4 Implementation of Digital Filter Banks......Page 842
10.9.5 Subband Coding of Speech Signals......Page 848
10.9.6 Quadrature Mlrror Filters......Page 850
10.9.7 Transmultiplexers......Page 858
10.9.8 Oversampling A/D & D/A Conversion......Page 860
10.10 Summary & References......Page 861
Problems......Page 863
11.1 Innovations Representation of Statlonary Random Process......Page 869
11.1.1 Rational Power Spectra......Page 871
11.1.2 Relationships between Filter Parameters & Autocorrelation Sequence......Page 872
11.2.1 Forward Linear Prediction......Page 874
11.2.2 Backward Linear Prediction......Page 877
11.2.3 Optimum Reflection Coefficients for Lattice Forward & Backward Predictors......Page 880
11.3 Solution of Normal Equations......Page 881
11.3.1 Levinson-Durbin Algorithm......Page 882
11.3.2 Schuer Algorithm......Page 885
11.4 Properties of Linear Prediction-Error Filters......Page 890
11.5 AR Lattice & ARMA Lattice-Ladder Filters......Page 893
11.5.1 AR Lattice Structure......Page 894
11.5.2 ARMA Processes & Lattice-Ladder Filters......Page 895
11.6 Wiener Filters for Filtering & Prediction......Page 897
11.6.1 FIR Wiener Filter......Page 898
11.6.2 Orthogonality Principle in Linear Mean-Square
Estimation......Page 901
11.6.3 IIR Wiener Filter......Page 902
11.6.4 Noncausal Wiener Filter......Page 906
11.7 Summary & References......Page 907
Problems......Page 909
12.1 Estimation of Spectra from Finite-Duration Observatlons of Signals......Page 913
12.1.1 Computation of Energy Density Spectrum......Page 914
12.1.2 Estimation of Autocorrelation & Power Spectrum of Random Signals: Periodogram......Page 919
12.1.3 Use of DFT in Power Spectrum Estimation......Page 923
12.2 Nonparametric Methods for Power Spectrum Estimation......Page 925
12.2.1 Bartlett Method: Averaging Periodograms......Page 927
12.2.2 Welch Method: Averaging Modified Periodograrns......Page 928
12.2.3 Blackman & Tukey Method: Smoothing Periodogram......Page 930
12.2.4 Performance Characteristics of Nonparametric
Power Spectrum Estimators......Page 933
12.2.5 Computational Requirements of Nonpararnetric
Power Spectrum Estimates......Page 936
12.3 Parametric Methods for Power Spectrum Estimation......Page 937
12.3.1 Relationships between Autocorrelation & Model Parameters......Page 940
12.3.3 Burg Method for AR Model Parameters......Page 942
12.3.4 Unconstrained Least-Squares Method for AR Model Parameters......Page 946
12.3.5 Sequential Estimation Methods for AR Model Parameters......Page 947
12.3.6 Selection of AR Model Order......Page 948
12.3.7 MA Model for Power Spectrum Estimation......Page 950
12.3.8 ARMA Model for Power Spectrum Estimation......Page 951
12.3.9 Some Experimental Results......Page 953
12.4 Minimum Variance Spectral Estimation......Page 959
12.5 Eigenanalysis Algorithms for Spectrum Estimation......Page 963
12.5.1 Pisarenko Harmonic Decomposition Method......Page 965
12.5.2 Eigen-Decomposition of Autocorrelation Matrix for Slnusoids in White Noise......Page 967
12.5.3 MUSIC Algorithm......Page 969
12.5.4 ESPRIT Algorithm......Page 970
12.5.5 Order Selection Criteria......Page 972
12.5.6 Experimental Results......Page 973
12.6 Summary & References......Page 976
Problems......Page 977
Random Processes......Page 986
Stationary Random Processes......Page 987
Statistical (Ensemble) Averages......Page 988
Statistical Averages for Joint Random Processes......Page 989
Power Density Spectrum......Page 990
Discrete-Time Random Signals......Page 991
Mean-Ergodic Process......Page 993
Correlation-Ergodic Processes......Page 994
AppB Random Number Generators......Page 996
AppC Tables of Transition Coefficients for Design of Linear-Phase FIR Filters......Page 1002
Ch1......Page 1008
Ch2-Ch3......Page 1009
Ch4-Ch7......Page 1010
Ch8......Page 1011
Ch9-Ch10......Page 1013
References & Bibliography......Page 1014
Index......Page 1029