导语

  

内容提要

  

    本书系统论述了离散时间信号处理的基本理论和方法，是国际信号处理领域中的经典教材。内容包括离散时间信号与系统，z变换，连续时间信号采样，线性时不变系统的变换分析，离散时间系统结构，滤波器设计方法，离散傅里叶变换，离散傅里叶变换的计算，利用离散傅里叶变换的信号傅里叶分析，参数信号建模，离散希尔伯特变换，倒谱分析与同态解卷积。本书例题和习题丰富，具有实用价值。模，离散希尔伯特变换，倒谱分析和同态解卷积。本书例题和习题丰富，具有实用价值。已根据作者发布的勘误表（更新至2012年10月29日）对书中内容做了相应的修改。
    本书适合从事数字信号处理工作的科技人员，高等学校相关专业的高年级学生、研究生及教师使用。

1  Introduction
2  Discrete-Time Signals and Systems
  2.0  Introduction
  2.1  Discrete-Time Signals
  2.2  Discrete-Time Systems
    2.2.1  Memoryless Systems
    2.2.2  Linear Systems
    2.2.3  Time-Invariant Systems
    2.2.4  Causality
    2.2.5  Stability
  2.3  LTI Systems
  2.4  Properties of Linear Time-Invariant Systems
  2.5  Linear Constant-Coefficient Difference Equations
  2.6  Frequency-Domain Representation of Discrete-Time Signals and Systems
    2.6.1  Eigenfunctions for Linear Time-Invariant Systems
    2.6.2  Suddenly Applied Complex Exponential Inputs
  2.7  Representation of Sequences by Fourier Transforms
  2.8  Symmetry Properties of the Fourier Transform
  2.9  Fourier Transform Theorems
    2.9.1  Linearity of the Fourier Transform
    2.9.2  Time Shifting and Frequency Shifting Theorem
    2.9.3  Time Reversal Theorem
    2.9.4  Differentiation in Frequency Theorem
    2.9.5  Parseval’s Theorem
    2.9.6  The Convolution Theorem
    2.9.7  The Modulation or Windowing Theorem
  2.10  Discrete-Time Random Signals
  2.11  Summary
  Problems
3  The z-Transform
  3.0  Introduction
  3.1  z-Transform
  3.2  Properties of the ROC for the z-Transform
  3.3  The Inverse z-Transform
    3.3.1  Inspection Method
    3.3.2  Partial Fraction Expansion
    3.3.3  Power Series Expansion
  3.4  z-Transform Properties
    3.4.1  Linearity
    3.4.2  Time Shifting
    3.4.3  Multiplication by an Exponential Sequence
    3.4.4  Differentiation of X(z)
    3.4.5  Conjugation of a Complex Sequence
    3.4.6  Time Reversal
    3.4.7  Convolution of Sequences
    3.4.8  Summary of Some z-Transform Properties
  3.5  z-Transforms and LTI Systems
  3.6  The Unilateral z-Transform
  3.7  Summary
  Problems
4  Sampling of Continuous-Time Signals
  4.0  Introduction
  4.1  Periodic Sampling
  4.2  Frequency-Domain Representation of Sampling
  4.3  Reconstruction of a Bandlimited Signal from Its Samples
  4.4  Discrete-Time Processing of Continuous-Time Signals
    4.4.1  Discrete-Time LTI Processing of Continuous-Time Signals
    4.4.2  Impulse Invariance
  4.5  Continuous-Time Processing of Discrete-Time Signals
  4.6  Changing the Sampling Rate Using Discrete-Time Processing
    4.6.1  Sampling Rate Reduction by an Integer Factor
    4.6.2  Increasing the Sampling Rate by an Integer Factor
    4.6.3  Simple and Practical Interpolation Filters
    4.6.4  Changing the Sampling Rate by a Noninteger Factor
  4.7  Multirate Signal Processing
    4.7.1  Interchange of Filtering with Compressor/Expander
    4.7.2  Multistage Decimation and Interpolation
    4.7.3  Polyphase Decompositions
    4.7.4  Polyphase Implementation of Decimation Filters
    4.7.5  Polyphase Implementation of Interpolation Filters
    4.7.6  Multirate Filter Banks
  4.8  Digital Processing of Analog Signals
    4.8.1  Prefiltering to Avoid Aliasing
    4.8.2  A/D Conversion
    4.8.3  Analysis of Quantization Errors
    4.8.4  D/A Conversion
  4.9  Oversampling and Noise Shaping in A/D and D/A Conversion
    4.9.1  Oversampled A/D Conversion with Direct Quantization
    4.9.2  Oversampled A/D Conversion with Noise Shaping
    4.9.3  Oversampling and Noise Shaping in D/A Conversion
  4.10  Summary
  Problems
5  Transform Analysis of Linear Time-Invariant Systems
  5.0  Introduction
  5.1  The Frequency Response of LTI Systems
    5.1.1  Frequency Response Phase and Group Delay
    5.1.2  Illustration of Effects of Group Delay and Attenuation
  5.2  System Functions—Linear Constant-Coefficient Difference Equations
    5.2.1  Stability and Causality
    5.2.2  Inverse Systems
    5.2.3  Impulse Response for Rational System Functions
  5.3  Frequency Response for Rational System Functions
    5.3.1  Frequency Response of 1st-Order Systems
    5.3.2  Examples with Multiple Poles and Zeros
  5.4  Relationship between Magnitude and Phase
  5.5  All-Pass Systems
  5.6  Minimum-Phase Systems
    5.6.1  Minimum-Phase and All-Pass Decomposition
    5.6.2  Frequency-Response Compensation of Non-Minimum-Phase Systems
    5.6.3  Properties of Minimum-Phase Systems
  5.7  Linear Systems with Generalized Linear Phase
    5.7.1  Systems with Linear Phase
    5.7.2  Generalized Linear Phase
    5.7.3  Causal Generalized Linear-Phase Systems
    5.7.4  Relation of FIR Linear-Phase Systems to Minimum-Phase Systems
  5.8  Summary
  Problems
6  Structures for Discrete-Time Systems
  6.0  Introduction
  6.1  Block Diagram Representation of Linear Constant-Coefficient Difference Equations
  6.2  Signal Flow Graph Representation
  6.3  Basic Structures for IIR Systems
    6.3.1  Direct Forms
    6.3.2  Cascade Form
    6.3.3  Parallel Form
    6.3.4  Feedback in IIR Systems
  6.4  Transposed Forms
  6.5  Basic Network Structures for FIR Systems
    6.5.1  Direct Form
    6.5.2  Cascade Form
    6.5.3  Structures for Linear-Phase FIR Systems
  6.6  Lattice Filters
    6.6.1  FIR Lattice Filters
    6.6.2  All-Pole Lattice Structure
    6.6.3  Generalization of Lattice Systems
  6.7  Overview of Finite-Precision Numerical Effects
    6.7.1  Number Representations
    6.7.2  Quantization in Implementing Systems
  6.8  The Effects of Coefficient Quantization
    6.8.1  Effects of Coefficient Quantization in IIR Systems
    6.8.2  Example of Coefficient Quantization in an Elliptic Filter
    6.8.3  Poles of Quantized 2nd-Order Sections
    6.8.4  Effects of Coefficient Quantization in FIR Systems
    6.8.5  Example of Quantization of an Optimum FIR Filter
    6.8.6  Maintaining Linear Phase
  6.9  Effects of Round-off Noise in Digital Filters
    6.9.1  Analysis of the Direct Form IIR Structures
    6.9.2  Scaling in Fixed-Point Implementations of IIR Systems
    6.9.3  Example of Analysis of a Cascade IIR Structure
    6.9.4  Analysis of Direct-Form FIR Systems
    6.9.5  Floating-Point Realizations of Discrete-Time Systems
  6.10  Zero-Input Limit Cycles in Fixed-Point Realizations of IIR Digital Filters
    6.10.1  Limit Cycles Owing to Round-off and Truncation
    6.10.2  Limit Cycles Owing to Overflow
    6.10.3  Avoiding Limit Cycles
  6.11  Summary
  Problems
7  Filter Design Techniques
  7.0  Introduction
  7.1  Filter Specifications
  7.2  Design of Discrete-Time IIR Filters from Continuous-Time Filters
    7.2.1  Filter Design by Impulse Invariance
    7.2.2  Bilinear Transformation
  7.3  Discrete-Time Butterworth, Chebyshev and Elliptic Filters
    7.3.1  Examples of IIR Filter Design
  7.4  Frequency Transformations of Lowpass IIR Filters
  7.5  Design of FIR Filters by Windowing
    7.5.1  Properties of Commonly Used Windows
    7.5.2  Incorporation of Generalized Linear Phase
    7.5.3  The KaiserWindow Filter Design Method
  7.6  Examples of FIR Filter Design by the KaiserWindow Method
    7.6.1  Lowpass Filter
    7.6.2  Highpass Filter
    7.6.3  Discrete-Time Differentiators
  7.7  Optimum Approximations of FIR Filters
    7.7.1  Optimal Type I Lowpass Filters
    7.7.2  Optimal Type II Lowpass Filters
    7.7.3  The Parks–McClellan Algorithm
    7.7.4  Characteristics of Optimum FIR Filters
  7.8  Examples of FIR Equiripple Approximation
    7.8.1  Lowpass Filter
    7.8.2  Compensation for Zero-Order Hold
    7.8.3  Bandpass Filter
  7.9  Comments on IIR and FIR Discrete-Time Filters
  7.10  Design of an Upsampling Filter
  7.11  Summary
  Problems
8  The Discrete Fourier Transform
  8.0  Introduction
  8.1  Representation of Periodic Sequences: The Discrete Fourier Series
  8.2  Properties of the DFS
    8.2.1  Linearity
    8.2.2  Shift of a Sequence
    8.2.3  Duality
    8.2.4  Symmetry Properties
    8.2.5  Periodic Convolution
    8.2.6  Summary of Properties of the DFS Representation of Periodic Sequences
  8.3  The Fourier Transform of Periodic Signals
  8.4  Sampling the Fourier Transform
  8.5  Fourier Representation of Finite-Duration Sequences
  8.6  Properties of the DFT
    8.6.1  Linearity
    8.6.2  Circular Shift of a Sequence
    8.6.3  Duality
    8.6.4  Symmetry Properties
    8.6.5  Circular Convolution
    8.6.6  Summary of Properties of the DFT
  8.7  Linear Convolution Using the DFT
    8.7.1  Linear Convolution of Two Finite-Length Sequences
    8.7.2  Circular Convolution as Linear Convolution with Aliasing
    8.7.3  Implementing Linear Time-Invariant Systems Using the DFT
  8.8  The Discrete Cosine Transform (DCT)
    8.8.1  Definitions of the DCT
    8.8.2  Definition of the DCT-1 and DCT-
    8.8.3  Relationship between the DFT and the DCT-
    8.8.4  Relationship between the DFT and the DCT-
    8.8.5  Energy Compaction Property of the DCT-
    8.8.6  Applications of the DCT
  8.9  Summary
  Problems
9  Computation of the Discrete Fourier Transform
  9.0  Introduction
  9.1  Direct Computation of the Discrete Fourier Transform
    9.1.1  Direct Evaluation of the Definition of the DFT
    9.1.2  The Goertzel Algorithm
    9.1.3  Exploiting both Symmetry and Periodicity
  9.2  Decimation-in-Time FFT Algorithms
    9.2.1  Generalization and Programming the FFT
    9.2.2  In-Place Computations
    9.2.3  Alternative Forms
  9.3  Decimation-in-Frequency FFT Algorithms
    9.3.1  In-Place Computation
    9.3.2  Alternative Forms
  9.4  Practical Considerations
    9.4.1  Indexing
    9.4.2  Coefficients
  9.5  More General FFT Algorithms
    9.5.1  Algorithms for Composite Values of N
    9.5.2  Optimized FFT Algorithms
  9.6  Implementation of the DFT Using Convolution
    9.6.1  Overview of the Winograd Fourier Transform Algorithm
    9.6.2  The Chirp Transform Algorithm
  9.7  Effects of Finite Register Length
  9.8  Summary
  Problems
10  Fourier Analysis of Signals Using the Discrete Fourier Transform
  10.0  Introduction
  10.1  Fourier Analysis of Signals Using the DFT
  10.2  DFT Analysis of Sinusoidal Signals
    10.2.1  The Effect of Windowing
    10.2.2  Properties of the Windows
    10.2.3  The Effect of Spectral Sampling
  10.3  The Time-Dependent Fourier Transform
    10.3.1  Invertibility of X[n,)
    10.3.2  Filter Bank Interpretation of X[n,)
    10.3.3  The Effect of the Window
    10.3.4  Sampling in Time and Frequency
    10.3.5  The Overlap–Add Method of Reconstruction
    10.3.6  Signal Processing Based on the Time-Dependent Fourier Transform
    10.3.7  Filter Bank Interpretation of the Time-Dependent Fourier Transform
  10.4  Examples of Fourier Analysis of Nonstationary Signals
    10.4.1  Time-Dependent Fourier Analysis of Speech Signals
    10.4.2  Time-Dependent Fourier Analysis of Radar Signals
  10.5  Fourier Analysis of Stationary Random Signals: the Periodogram
    10.5.1  The Periodogram
    10.5.2  Properties of the Periodogram
    10.5.3  Periodogram Averaging
    10.5.4  Computation of Average Periodograms Using the DFT
    10.5.5  An Example of Periodogram Analysis
  10.6  Spectrum Analysis of Random Signals
    10.6.1  Computing Correlation and Power Spectrum Estimates Using theDFT
    10.6.2  Estimating the Power Spectrum of Quantization Noise
    10.6.3  Estimating the Power Spectrum of Speech
  10.7  Summary
  Problems
11  Parametric Signal Modeling
  11.0  Introduction
  11.1  All-Pole Modeling of Signals
    11.1.1  Least-Squares Approximation
    11.1.2  Least-Squares Inverse Model
    11.1.3  Linear Prediction Formulation of All-Pole Modeling
  11.2  Deterministic and Random Signal Models
    11.2.1  All-Pole Modeling of Finite-Energy Deterministic Signals
    11.2.2  Modeling of Random Signals
    11.2.3  Minimum Mean-Squared Error
    11.2.4  Autocorrelation Matching Property
    11.2.5  Determination of the Gain Parameter G
  11.3  Estimation of the Correlation Functions
    11.3.1  The Autocorrelation Method
    11.3.2  The Covariance Method
    11.3.3  Comparison of Methods
  11.4  Model Order
  11.5  All-Pole Spectrum Analysis
    11.5.1  All-Pole Analysis of Speech Signals
    11.5.2  Pole Locations
    11.5.3  All-Pole Modeling of Sinusoidal Signals
  11.6  Solution of the Autocorrelation Normal Equations
    11.6.1  The Levinson–Durbin Recursion
    11.6.2  Derivation of the Levinson–Durbin Algorithm
  11.7  Lattice Filters
    11.7.1  Prediction Error Lattice Network
    11.7.2  All-Pole Model Lattice Network
    11.7.3  Direct Computation of the k-Parameters
  11.8  Summary
  Problems
12  Discrete Hilbert Transforms
  12.0  Introduction
  12.1  Real- and Imaginary-Part Sufficiency of the Fourier Transform
  12.2  Sufficiency Theorems for Finite-Length Sequences
  12.3  Relationships Between Magnitude and Phase
  12.4  Hilbert Transform Relations for Complex Sequences
    12.4.1  Design of Hilbert Transformers
    12.4.2  Representation of Bandpass Signals
    12.4.3  Bandpass Sampling
  12.5  Summary
  Problems
13  Cepstrum Analysis and Homomorphic Deconvolution
  13.0  Introduction
  13.1  Definition of the Cepstrum
  13.2  Definition of the Complex Cepstrum
  13.3  Properties of the Complex Logarithm
  13.4  Alternative Expressions for the Complex Cepstrum
  13.5  Properties of the Complex Cepstrum
    13.5.1  Exponential Sequences
    13.5.2  Minimum-Phase and Maximum-Phase Sequences
    13.5.3  Relationship Between the Real Cepstrum and the Complex Cepstrum
  13.6  Computation of the Complex Cepstrum
    13.6.1  Phase Unwrapping
    13.6.2  Computation of the Complex Cepstrum Using the Logarithmic Derivative
    13.6.3  Minimum-Phase Realizations for Minimum-Phase Sequences
    13.6.4  Recursive Computation of theComplexCepstrum forMinimumand Maximum-Phase Sequences
    13.6.5  The Use of Exponential Weighting
  13.7  Computation of the Complex Cepstrum Using Polynomial Roots
  13.8  Deconvolution Using the Complex Cepstrum
    13.8.1  Minimum-Phase/Allpass Homomorphic Deconvolution
    13.8.2  Minimum-Phase/Maximum-Phase Homomorphic Deconvolution
  13.9  The Complex Cepstrum for a Simple Multipath Model
    13.9.1  Computation of the Complex Cepstrum by z-Transform Analysis
    13.9.2  Computation of the Cepstrum Using the DFT
    13.9.3  Homomorphic Deconvolution for the Multipath Model
    13.9.4  Minimum-Phase Decomposition
    13.9.5  Generalizations
  13.10  Applications to Speech Processing
    13.10.1  The Speech Model
    13.10.2  Example of Homomorphic Deconvolution of Speech
    13.10.3  Estimating the Parameters of the Speech Model
    13.10.4  Applications
  13.11  Summary
  Problems
A  Random Signals
B  Continuous-Time Filters
C  Answers to Selected Basic Problems
Bibliography
Index