Digital Signal Processing

by Proakis, John G.; Manolakis, Dimitris K

• ISBN13: 9780131873742
• ISBN10: 0131873741
• Edition: 4th
• Format: Paperback
• Copyright: 2006-03-28
• Publisher: Pearson

Summary

This fourth edition covers the fundamentals of discrete-time signals, systems, and modern digital signal processing. Appropriate for students of electrical engineering, computer engineering, and computer science, the book is suitable for undergraduate and graduate courses and provides balanced coverage of both theory and practical applications.

Table of Contents

Preface	p. xvii
Introduction	p. 1
Signals, Systems, and Signal Processing	p. 2
Basic Elements of a Digital Signal Processing System	p. 4
Advantages of Digital over Analog Signal Processing	p. 5
Classification of Signals	p. 6
Multichannel and Multidimensional Signals	p. 6
Continuous-Time Versus Discrete-Time Signals	p. 9
Continuous-Valued Versus Discrete-Valued Signals	p. 10
Deterministic Versus Random Signals	p. 11
The Concept of Frequency in Continuous-Time and Discrete-Time Signals	p. 12
Continuous-Time Sinusoidal Signals	p. 12
Discrete-Time Sinusoidal Signals	p. 14
Harmonically Related Complex Exponentials	p. 17
Analog-to-Digital and Digital-to-Analog Conversion	p. 19
Sampling of Analog Signals	p. 21
The Sampling Theorem	p. 26
Quantization of Continuous-Amplitude Signals	p. 31
Quantization of Sinusoidal Signals	p. 34
Coding of Quantized Samples	p. 35
Digital-to-Analog Conversion	p. 36
Analysis of Digital Signals and Systems Versus Discrete-Time Signals and Systems	p. 36
Summary and References	p. 37
Problems	p. 37
Discrete-Time Signals and Systems	p. 41
Discrete-Time Signals	p. 42
Some Elementary Discrete-Time Signals	p. 43
Classification of Discrete-Time Signals	p. 45
Simple Manipulations of Discrete-Time Signals	p. 50
Discrete-Time Systems	p. 53
Input-Output Description of Systems	p. 54
Block Diagram Representation of Discrete-Time Systems	p. 57
Classification of Discrete-Time Systems	p. 59
Interconnection of Discrete-Time Systems	p. 67
Analysis of Discrete-Time Linear Time-Invariant Systems	p. 69
Techniques for the Analysis of Linear Systems	p. 69
Resolution of a Discrete-Time Signal into Impulses	p. 71
Response of LTI Systems to Arbitrary Inputs: The Convolution Sum	p. 73
Properties of Convolution and the Interconnection of LTI Systems	p. 80
Causal Linear Time-Invariant Systems	p. 83
Stability of Linear Time-Invariant Systems	p. 85
Systems with Finite-Duration and Infinite-Duration Impulse Response	p. 88
Discrete-Time Systems Described by Difference Equations	p. 89
Recursive and Nonrecursive Discrete-Time Systems	p. 90
Linear Time-Invariant Systems Characterized by Constant-Coefficient Difference Equations	p. 93
Solution of Linear Constant-Coefficient Difference Equations	p. 98
The Impulse Response of a Linear Time-Invariant Recursive System	p. 106
Implementation of Discrete-Time Systems	p. 109
Structures for the Realization of Linear Time-Invariant Systems	p. 109
Recursive and Nonrecursive Realizations of FIR Systems	p. 113
Correlation of Discrete-Time Signals	p. 116
Crosscorrelation and Autocorrelation Sequences	p. 118
Properties of the Autocorrelation and Crosscorrelation Sequences	p. 120
Correlation of Periodic Sequences	p. 123
Input-Output Correlation Sequences	p. 125
Summary and References	p. 128
Problems	p. 129
The z-Transform and Its Application to the Analysis of LTI Systems	p. 147
The z-Transform	p. 147
The Direct z-Transform	p. 147
The Inverse z-Transform	p. 156
Properties of the z-Transform	p. 157
Rational z-Transforms	p. 170
Poles and Zeros	p. 170
Pole Location and Time-Domain Behavior for Causal Signals	p. 174
The System Function of a Linear Time-Invariant System	p. 177
Inversion of the z-Transform	p. 180
The Inverse z-Transform by Contour Integration	p. 180
The Inverse z-Transform by Power Series Expansion	p. 182
The Inverse z-Transform by Partial-Fraction Expansion	p. 184
Decomposition of Rational z-Transforms	p. 192
Analysis of Linear Time-Invariant Systems in the z-Domain	p. 193
Response of Systems with Rational System Functions	p. 194
Transient and Steady-State Responses	p. 195
Causality and Stability	p. 196
Pole-Zero Cancellations	p. 198
Multiple-Order Poles and Stability	p. 200
Stability of Second-Order Systems	p. 201
The One-sided z-Transform	p. 205
Definition and Properties	p. 206
Solution of Difference Equations	p. 210
Response of Pole-Zero Systems with Nonzero Initial Conditions	p. 211
Summary and References	p. 214
Problems	p. 214
Frequency Analysis of Signals	p. 224
Frequency Analysis of Continuous-Time Signals	p. 225
The Fourier Series for Continuous-Time Periodic Signals	p. 226
Power Density Spectrum of Periodic Signals	p. 230
The Fourier Transform for Continuous-Time Aperiodic Signals	p. 234
Energy Density Spectrum of Aperiodic Signals	p. 238
Frequency Analysis of Discrete-Time Signals	p. 241
The Fourier Series for Discrete-Time Periodic Signals	p. 241
Power Density Spectrum of Periodic Signals	p. 245
The Fourier Transform of Discrete-Time Aperiodic Signals	p. 248
Convergence of the Fourier Transform	p. 251
Energy Density Spectrum of Aperiodic Signals	p. 254
Relationship of the Fourier Transform to the z-Transform	p. 259
The Cepstrum	p. 261
The Fourier Transform of Signals with Poles on the Unit Circle	p. 262
Frequency-Domain Classification of Signals: The Concept of Bandwidth	p. 265
The Frequency Ranges of Some Natural Signals	p. 267
Frequency-Domain and Time-Domain Signal Properties	p. 268
Properties of the Fourier Transform for Discrete-Time Signals	p. 271
Symmetry Properties of the Fourier Transform	p. 272
Fourier Transform Theorems and Properties	p. 279
Summary and References	p. 291
Problems	p. 292
Frequency-Domain Analysis of LTI Systems	p. 300
Frequency-Domain Characteristics of Linear Time-Invariant Systems	p. 300
Response to Complex Exponential and Sinusoidal Signals: The Frequency Response Function	p. 301
Steady-State and Transient Response to Sinusoidal Input Signals	p. 310
Steady-State Response to Periodic Input Signals	p. 311
Response to Aperiodic Input Signals	p. 312
Frequency Response of LTI Systems	p. 314
Frequency Response of a System with a Rational System Function	p. 314
Computation of the Frequency Response Function	p. 317
Correlation Functions and Spectra at the Output of LTI Systems	p. 321
Input-Output Correlation Functions and Spectra	p. 322
Correlation Functions and Power Spectra for Random Input Signals	p. 323
Linear Time-Invariant Systems as Frequency-Selective Filters	p. 326
Ideal Filter Characteristics	p. 327
Lowpass, Highpass, and Bandpass Filters	p. 329
Digital Resonators	p. 335
Notch Filters	p. 339
Comb Filters	p. 341
All-Pass Filters	p. 345
Digital Sinusoidal Oscillators	p. 347
Inverse Systems and Deconvolution	p. 349
Invertibility of Linear Time-Invariant Systems	p. 350
Minimum-Phase, Maximum-Phase, and Mixed-Phase Systems	p. 354
System Identification and Deconvolution	p. 358
Homomorphic Deconvolution	p. 360
Summary and References	p. 362
Problems	p. 363
Sampling and Reconstruction of Signals	p. 384
Ideal Sampling and Reconstruction of Continuous-Time Signals	p. 384
Discrete-Time Processing of Continuous-Time Signals	p. 395
Analog-to-Digital and Digital-to-Analog Converters	p. 401
Analog-to-Digital Converters	p. 401
Quantization and Coding	p. 403
Analysis of Quantization Errors	p. 406
Digital-to-Analog Converters	p. 408
Sampling and Reconstruction of Continuous-Time Bandpass Signals	p. 410
Uniform or First-Order Sampling	p. 411
Interleaved or Nonuniform Second-Order Sampling	p. 416
Bandpass Signal Representations	p. 422
Sampling Using Bandpass Signal Representations	p. 426
Sampling of Discrete-Time Signals	p. 427
Sampling and Interpolation of Discrete-Time Signals	p. 427
Representation and Sampling of Bandpass Discrete-Time Signals	p. 430
Oversampling A/D and D/A Converters	p. 433
Oversampling A/D Converters	p. 433
Oversampling D/A Converters	p. 439
Summary and References	p. 440
Problems	p. 440
The Discrete Fourier Transform: Its Properties and Applications	p. 449
Frequency-Domain Sampling: The Discrete Fourier Transform	p. 449
Frequency-Domain Sampling and Reconstruction of Discrete-Time Signals	p. 449
The Discrete Fourier Transform (DFT)	p. 454
The DFT as a Linear Transformation	p. 459
Relationship of the DFT to Other Transforms	p. 461
Properties of the DFT	p. 464
Periodicity, Linearity, and Symmetry Properties	p. 465
Multiplication of Two DFTs and Circular Convolution	p. 471
Additional DFT Properties	p. 476
Linear Filtering Methods Based on the DFT	p. 480
Use of the DFT in Linear Filtering	p. 481
Filtering of Long Data Sequences	p. 485
Frequency Analysis of Signals Using the DFT	p. 488
The Discrete Cosine Transform	p. 495
Forward DCT	p. 495
Inverse DCT	p. 497
DCT as an Orthogonal Transform	p. 498
Summary and References	p. 501
Problems	p. 502
Efficient Computation of the DFT: Fast Fourier Transform Algorithms	p. 511
Efficient Computation of the DFT: FFT Algorithms	p. 511
Direct Computation of the DFT	p. 512
Divide-and-Conquer Approach to Computation of the DFT	p. 513
Radix-2 FFT Algorithms	p. 519
Radix-4 FFT Algorithms	p. 527
Split-Radix FFT Algorithms	p. 532
Implementation of FFT Algorithms	p. 536
Applications of FFT Algorithms	p. 538
Efficient Computation of the DFT of Two Real Sequences	p. 538
Efficient Computation of the DFT of a 2N-Point Real Sequence	p. 539
Use of the FFT Algorithm in Linear Filtering and Correlation	p. 540
A Linear Filtering Approach to Computation of the DFT	p. 542
The Goertzel Algorithm	p. 542
The Chirp-z Transform Algorithm	p. 544
Quantization Effects in the Computation of the DFT	p. 549
Quantization Errors in the Direct Computation of the DFT	p. 549
Quantization Errors in FFT Algorithms	p. 552
Summary and References	p. 555
Problems	p. 556
Implementation of Discrete-Time Systems	p. 563
Structures for the Realization of Discrete-Time Systems	p. 563
Structures for FIR Systems	p. 565
Direct-Form Structure	p. 566
Cascade-Form Structures	p. 567
Frequency-Sampling Structures	p. 569
Lattice Structure	p. 574
Structures for IIR Systems	p. 582
Direct-Form Structures	p. 582
Signal Flow Graphs and Transposed Structures	p. 585
Cascade-Form Structures	p. 589
Parallel-Form Structures	p. 591
Lattice and Lattice-Ladder Structures for IIR Systems	p. 594
Representation of Numbers	p. 601
Fixed-Point Representation of Numbers	p. 601
Binary Floating-Point Representation of Numbers	p. 605
Errors Resulting from Rounding and Truncation	p. 608
Quantization of Filter Coefficients	p. 613
Analysis of Sensitivity to Quantization of Filter Coefficients	p. 613
Quantization of Coefficients in FIR Filters	p. 620
Round-Off Effects in Digital Filters	p. 624
Limit-Cycle Oscillations in Recursive Systems	p. 624
Scaling to Prevent Overflow	p. 629
Statistical Characterization of Quantization Effects in Fixed-Point Realizations of Digital Filters	p. 631
Summary and References	p. 640
Problems	p. 641
Design of Digital Filters	p. 654
General Considerations	p. 654
Causality and Its Implications	p. 655
Characteristics of Practical Frequency-Selective Filters	p. 659
Design of FIR Filters	p. 660
Symmetric and Antisymmetric FIR Filters	p. 660
Design of Linear-Phase FIR Filters Using Windows	p. 664
Design of Linear-Phase FIR Filters by the Frequency-Sampling Method	p. 671
Design of Optimum Equiripple Linear-Phase FIR Filters	p. 678
Design of FIR Differentiators	p. 691
Design of Hilbert Transformers	p. 693
Comparison of Design Methods for Linear-Phase FIR Filters	p. 700
Design of IIR Filters From Analog Filters	p. 701
IIR Filter Design by Approximation of Derivatives	p. 703
IIR Filter Design by Impulse Invariance	p. 707
IIR Filter Design by the Bilinear Transformation	p. 712
Characteristics of Commonly Used Analog Filters	p. 717
Some Examples of Digital Filter Designs Based on the Bilinear Transformation	p. 727
Frequency Transformations	p. 730
Frequency Transformations in the Analog Domain	p. 730
Frequency Transformations in the Digital Domain	p. 732
Summary and References	p. 734
Problems	p. 735
Multirate Digital Signal Processing	p. 750
Introduction	p. 751
Decimation by a Factor D	p. 755
Interpolation by a Factor I	p. 760
Sampling Rate Conversion by a Rational Factor I/D	p. 762
Implementation of Sampling Rate Conversion	p. 766
Polyphase Filter Structures	p. 766
Interchange of Filters and Downsamplers/Upsamplers	p. 767
Sampling Rate Conversion with Cascaded Integrator Comb Filters	p. 769
Polyphase Structures for Decimation and Interpolation Filters	p. 771
Structures for Rational Sampling Rate Conversion	p. 774
Multistage Implementation of Sampling Rate Conversion	p. 775
Sampling Rate Conversion of Bandpass Signals	p. 779
Sampling Rate Conversion by an Arbitrary Factor	p. 781
Arbitrary Resampling with Polyphase Interpolators	p. 782
Arbitrary Resampling with Farrow Filter Structures	p. 782
Applications of Multirate Signal Processing	p. 784
Design of Phase Shifters	p. 784
Interfacing of Digital Systems with Different Sampling Rates	p. 785
Implementation of Narrowband Lowpass Filters	p. 786
Subband Coding of Speech Signals	p. 787
Digital Filter Banks	p. 790
Polyphase Structures of Uniform Filter Banks	p. 794
Transmultiplexers	p. 796
Two-Channel Quadrature Mirror Filter Bank	p. 798
Elimination of Aliasing	p. 799
Condition for Perfect Reconstruction	p. 801
Polyphase Form of the QMF Bank	p. 801
Linear Phase FIR QMF Bank	p. 802
IIR QMF Bank	p. 803
Perfect Reconstruction Two-Channel FIR QMF Bank	p. 803
Two-Channel QMF Banks in Subband Coding	p. 806
M-Channel QMF Bank	p. 807
Alias-Free and Perfect Reconstruction Condition	p. 808
Polyphase Form of the M-Channel QMF Bank	p. 808
Summary and References	p. 813
Problems	p. 813
Linear Prediction and Optimum Linear Filters	p. 823
Random Signals, Correlation Functions, and Power Spectra	p. 823
Random Processes	p. 824
Stationary Random Processes	p. 825
Statistical (Ensemble) Averages	p. 825
Statistical Averages for Joint Random Processes	p. 826
Power Density Spectrum	p. 828
Discrete-Time Random Signals	p. 829
Time Averages for a Discrete-Time Random Process	p. 830
Mean-Ergodic Process	p. 831
Correlation-Ergodic Processes	p. 832
Innovations Representation of a Stationary Random Process	p. 834
Rational Power Spectra	p. 836
Relationships Between the Filter Parameters and the Autocorrelation Sequence	p. 837
Forward and Backward Linear Prediction	p. 838
Forward Linear Prediction	p. 839
Backward Linear Prediction	p. 841
The Optimum Reflection Coefficients for the Lattice Forward and Backward Predictors	p. 845
Relationship of an AR Process to Linear Prediction	p. 846
Solution of the Normal Equations	p. 846
The Levinson-Durbin Algorithm	p. 847
The Schur Algorithm	p. 850
Properties of the Linear Prediction-Error Filters	p. 855
AR Lattice and ARMA Lattice-Ladder Filters	p. 858
AR Lattice Structure	p. 858
ARMA Processes and Lattice-Ladder Filters	p. 860
Wiener Filters for Filtering and Prediction	p. 863
FIR Wiener Filter	p. 864
Orthogonality Principle in Linear Mean-Square Estimation	p. 866
IIR Wiener Filter	p. 867
Noncausal Wiener Filter	p. 872
Summary and References	p. 873
Problems	p. 874
Adaptive Filters	p. 880
Applications of Adaptive Filters	p. 880
System Identification or System Modeling	p. 882
Adaptive Channel Equalization	p. 883
Echo Cancellation in Data Transmission over Telephone Channels	p. 887
Suppression of Narrowband Interference in a Wideband Signal	p. 891
Adaptive Line Enhancer	p. 895
Adaptive Noise Cancelling	p. 896
Linear Predictive Coding of Speech Signals	p. 897
Adaptive Arrays	p. 900
Adaptive Direct-Form FIR Filters-The LMS Algorithm	p. 902
Minimum Mean-Square-Error Criterion	p. 903
The LMS Algorithm	p. 905
Related Stochastic Gradient Algorithms	p. 907
Properties of the LMS Algorithm	p. 909
Adaptive Direct-Form Filters-RLS Algorithms	p. 916
RLS Algorithm	p. 916
The LDU Factorization and Square-Root Algorithms	p. 921
Fast RLS Algorithms	p. 923
Properties of the Direct-Form RLS Algorithms	p. 925
Adaptive Lattice-Ladder Filters	p. 927
Recursive Least-Squares Lattice-Ladder Algorithms	p. 928
Other Lattice Algorithms	p. 949
Properties of Lattice-Ladder Algorithms	p. 950
Summary and References	p. 954
Problems	p. 955
Power Spectrum Estimation	p. 960
Estimation of Spectra from Finite-Duration Observations of Signals	p. 961
Computation of the Energy Density Spectrum	p. 961
Estimation of the Autocorrelation and Power Spectrum of Random Signals: The Periodogram	p. 966
The Use of the DFT in Power Spectrum Estimation	p. 971
Nonparametric Methods for Power Spectrum Estimation	p. 974
The Bartlett Method: Averaging Periodograms	p. 974
The Welch Method: Averaging Modified Periodograms	p. 975
The Blackman and Tukey Method: Smoothing the Periodogram	p. 978
Performance Characteristics of Nonparametric Power Spectrum Estimators	p. 981
Computational Requirements of Nonparametric Power Spectrum Estimates	p. 984
Parametric Methods for Power Spectrum Estimation	p. 986
Relationships Between the Autocorrelation and the Model Parameters	p. 988
The Yule-Walker Method for the AR Model Parameters	p. 990
The Burg Method for the AR Model Parameters	p. 991
Unconstrained Least-Squares Method for the AR Model Parameters	p. 994
Sequential Estimation Methods for the AR Model Parameters	p. 995
Selection of AR Model Order	p. 996
MA Model for Power Spectrum Estimation	p. 997
ARMA Model for Power Spectrum Estimation	p. 999
Some Experimental Results	p. 1001
Filter Bank Methods	p. 1009
Filter Bank Realization of the Periodogram	p. 1010
Minimum Variance Spectral Estimates	p. 1012
Eigenanalysis Algorithms for Spectrum Estimation	p. 1015
Pisarenko Harmonic Decomposition Method	p. 1017
Eigen-decomposition of the Autocorrelation Matrix for Sinusoids in White Noise	p. 1019
MUSIC Algorithm	p. 1021
ESPRIT Algorithm	p. 1022
Order Selection Criteria	p. 1025
Experimental Results	p. 1026
Summary and References	p. 1029
Problems	p. 1030
Random Number Generators	p. 1041
Tables of Transition Coefficients for the Design of Linear-Phase FIR Filters	p. 1047
References and Bibliography	p. 1053
Answers to Selected Problems	p. 1067
Index	p. 1077
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