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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