Digital Signal Processing: Principles, Algorithms and Applications, 5th edition
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Overview
Digital Signal Processing is your guide to the fundamental concepts and techniques of discretetime signals, systems, and modern digital processing. Related algorithms and applications are covered, as are both timedomain and frequencydomain methods for the analysis of linear, discretetime systems.
Published by Pearson (July 23rd 2021)  Copyright © 2022
ISBN13: 9780137348657
Subject: Electrical Engineering
Category: Digital Signals & Systems
Table of contents
Table of Contents
 Introduction
 1.1 Signals, Systems, and Signal Processing
 1.1.1 Basic Elements of a Digital Signal Processing System
 1.1.2 Advantages of Digital over Analog Signal Processing
 1.2 Classification of Signals
 1.2.1 Multichannel and Multidimensional Signals
 1.2.2 ContinuousTime Versus DiscreteTime Signals
 1.2.3 ContinuousValued Versus DiscreteValued Signals
 1.2.4 Deterministic Versus Random Signals
 1.3 Summary
 Problems
 1.1 Signals, Systems, and Signal Processing
 DiscreteTime Signals and Systems
 2.1 DiscreteTime Signals
 2.1.1 Some Elementary DiscreteTime Signals
 2.1.2 Classification of DiscreteTime Signals
 2.1.3 Simple Manipulations of DiscreteTime Signals
 2.2 DiscreteTime Systems
 2.2.1 InputOutput Description of Systems
 2.2.2 Block Diagram Representation of DiscreteTime Systems
 2.2.3 Classification of DiscreteTime Systems
 2.2.4 Interconnection of DiscreteTime Systems
 2.3 Analysis of DiscreteTime Linear TimeInvariant Systems
 2.3.1 Techniques for the Analysis of Linear Systems
 2.3.2 Resolution of a DiscreteTime Signal into Impulses
 2.3.3 Response of LTI Systems to Arbitrary Inputs: The Convolution Sum
 2.3.4 Properties of Convolution and the Interconnection of LTI Systems
 2.3.5 Causal Linear TimeInvariant Systems
 2.3.6 Stability of Linear TimeInvariant Systems
 2.3.7 Systems with FiniteDuration and InfiniteDuration Impulse Response
 2.4 DiscreteTime Systems Described by Difference Equations
 2.4.1 Recursive and Nonrecursive DiscreteTime Systems
 2.4.2 Linear TimeInvariant Systems Characterized by ConstantCoefficient Difference Equations
 2.4.3 Application of LTI Systems for Signal Smoothing
 2.5 Implementation of DiscreteTime Systems
 2.5.1 Structures for the Realization of Linear TimeInvariant Systems
 2.5.2 Recursive and Nonrecursive Realizations of FIR Systems
 2.6 Correlation of DiscreteTime Signals
 2.6.1 Crosscorrelation and Autocorrelation Sequences
 2.6.2 Properties of the Autocorrelation and Crosscorrelation Sequences
 2.6.3 Correlation of Periodic Sequences
 2.6.4 InputOutput Correlation Sequences
 2.7 Summary
 Problems
 Computer Problems
 2.1 DiscreteTime Signals
 The zTransform and Its Application to the Analysis of LTI Systems
 3.1 The zTransform
 3.1.1 The Direct zTransform
 3.1.2 The Inverse zTransform
 3.2 Properties of the zTransform
 3.3 Rational zTransforms
 3.3.1 Poles and Zeros
 3.3.2 Pole Location and TimeDomain Behavior for Causal Signals
 3.3.3 The System Function of a Linear TimeInvariant System
 3.4 Inversion of the zTransform
 3.4.1 The Inverse zTransform by Contour Integration
 3.4.2 The Inverse zTransform by Power Series Expansion
 3.4.3 The Inverse zTransform by PartialFraction Expansion
 3.4.4 Decomposition of Rational zTransforms
 3.5 Analysis of Linear TimeInvariant Systems in the zDomain
 3.5.1 Response of Systems with Rational System Functions
 3.5.2 Transient and SteadyState Responses
 3.5.3 Causality and Stability
 3.5.4 Pole—Zero Cancellations
 3.5.5 MultipleOrder Poles and Stability
 3.5.6 Stability of SecondOrder Systems
 3.6 The Onesided zTransform
 3.6.1 Definition and Properties
 3.6.2 Solution of Difference Equations
 3.6.3 Response of Pole—Zero Systems with Nonzero Initial Conditions
 3.7 Summary
 Problems
 Computer Problems
 3.1 The zTransform
 Frequency Analysis of Signals
 4.1 The Concept of Frequency in ContinuousTime and DiscreteTime Signals
 4.1.1 ContinuousTime Sinusoidal Signals
 4.1.2 DiscreteTime Sinusoidal Signals
 4.1.3 Harmonically Related Complex Exponentials
 4.1.4 Sampling of Analog Signals
 4.1.5 The Sampling Theorem
 4.2 Frequency Analysis of ContinuousTime Signals
 4.2.1 The Fourier Series for ContinuousTime Periodic Signals
 4.2.2 Power Density Spectrum of Periodic Signals
 4.2.3 The Fourier Transform for ContinuousTime Aperiodic Signals
 4.2.4 Energy Density Spectrum of Aperiodic Signals
 4.3 Frequency Analysis of DiscreteTime Signals
 4.3.1 The Fourier Series for DiscreteTime Periodic Signals
 4.3.2 Power Density Spectrum of Periodic Signals
 4.3.3 The Fourier Transform of DiscreteTime Aperiodic Signals
 4.3.4 Convergence of the Fourier Transform
 4.3.5 Energy Density Spectrum of Aperiodic Signals
 4.3.6 Relationship of the Fourier Transform to the zTransform
 4.3.7 The Cepstrum
 4.3.8 The Fourier Transform of Signals with Poles on the Unit Circle
 4.3.9 FrequencyDomain Classification of Signals: The Concept of Bandwidth
 4.3.10 The Frequency Ranges of Some Natural Signals
 4.4 FrequencyDomain and TimeDomain Signal Properties
 4.5 Properties of the Fourier Transform for DiscreteTime Signals
 4.5.1 Symmetry Properties of the Fourier Transform
 4.5.2 Fourier Transform Theorems and Properties
 4.6 Summary
 Problems
 Computer Problems
 4.1 The Concept of Frequency in ContinuousTime and DiscreteTime Signals
 FrequencyDomain Analysis of LTI Systems
 5.1 FrequencyDomain Characteristics of Linear TimeInvariant Systems
 5.1.1 Response to Complex Exponential and Sinusoidal Signals: The Frequency Response Function
 5.1.2 SteadyState and Transient Response to Sinusoidal Input Signals
 5.1.3 SteadyState Response to Periodic Input Signals
 5.1.4 SteadyState Response to Aperiodic Input Signals
 5.2 Frequency Response of LTI Systems
 5.2.1 Frequency Response of a System with a Rational System Function
 5.2.2 Computation of the Frequency Response Function
 5.3 Correlation Functions and Spectra at the Output of LTI Systems
 5.4 Linear TimeInvariant Systems as FrequencySelective Filters
 5.4.1 Ideal Filter Characteristics
 5.4.2 Lowpass, Highpass, and Bandpass Filters
 5.4.3 Digital Resonators
 5.4.4 Notch Filters
 5.4.5 Comb Filters
 5.4.6 Reverberation Filters
 5.4.7 AllPass Filters
 5.4.8 Digital Sinusoidal Oscillators
 5.5 Inverse Systems and Deconvolution
 5.5.1 Invertibility of Linear TimeInvariant Systems
 5.5.2 MinimumPhase, MaximumPhase, and MixedPhase Systems
 5.5.3 System Identification and Deconvolution
 5.5.4 Homomorphic Deconvolution
 5.6 Summary
 Problems
 Computer Problems
 5.1 FrequencyDomain Characteristics of Linear TimeInvariant Systems
 Sampling and Reconstruction of Signals
 6.1 Ideal Sampling and Reconstruction of ContinuousTime Signals
 6.2 DiscreteTime Processing of ContinuousTime Signals
 6.3 Sampling and Reconstruction of ContinuousTime Bandpass Signals
 6.3.1 Uniform or FirstOrder Sampling
 6.3.2 Interleaved or Nonuniform SecondOrder Sampling
 6.3.3 Bandpass Signal Representations
 6.3.4 Sampling Using Bandpass Signal Representations
 6.4 Sampling of DiscreteTime Signals
 6.4.1 Sampling and Interpolation of DiscreteTime Signals
 6.4.2 Representation and Sampling of Bandpass DiscreteTime Signals
 6.5 AnalogtoDigital and DigitaltoAnalog Converters
 6.5.1 AnalogtoDigital Converters
 6.5.2 Quantization and Coding
 6.5.3 Analysis of Quantization Errors
 6.5.4 DigitaltoAnalog Converters
 6.6 Oversampling A/D and D/A Converters
 6.6.1 Oversampling A/D Converters
 6.6.2 Oversampling D/A Converters
 6.7 Summary
 Problems
 Computer Problems
 The Discrete Fourier Transform: Its Properties and Applications
 7.1 FrequencyDomain Sampling: The Discrete Fourier Transform
 7.1.1 FrequencyDomain Sampling and Reconstruction of DiscreteTime Signals
 7.1.2 The Discrete Fourier Transform (DFT)
 7.1.3 The DFT as a Linear Transformation
 7.1.4 Relationship of the DFT to Other Transforms
 7.2 Properties of the DFT
 7.2.1 Periodicity, Linearity, and Symmetry Properties
 7.2.2 Multiplication of Two DFTs and Circular Convolution
 7.2.3 Additional DFT Properties
 7.3 Linear Filtering Methods Based on the DFT
 7.3.1 Use of the DFT in Linear Filtering
 7.3.2 Filtering of Long Data Sequences
 7.4 Frequency Analysis of Signals Using the DFT
 7.5 The ShortTime Fourier Transform
 7.6 The Discrete Cosine Transform
 7.6.1 Forward DCT
 7.6.2 Inverse DCT
 7.6.3 DCT as an Orthogonal Transform
 7.7 Summary
 Problems
 Computer Problems
 7.1 FrequencyDomain Sampling: The Discrete Fourier Transform
 Efficient Computation of the DFT: Fast Fourier Transform Algorithms
 8.1 Efficient Computation of the DFT: FFT Algorithms
 8.1.1 Direct Computation of the DFT
 8.1.2 DivideandConquer Approach to Computation of the DFT
 8.1.3 Radix2 FFT Algorithms
 8.1.4 Radix4 FFT Algorithms
 8.1.5 SplitRadix FFT Algorithms
 8.1.6 Implementation of FFT Algorithms
 8.1.7 Sparse FFT Algorithm
 8.2 Applications of FFT Algorithms
 8.2.1 Efficient Computation of the DFT of Two Real Sequences
 8.2.2 Efficient Computation of the DFT of a 2NPoint Real Sequence
 8.2.3 Use of the FFT Algorithm in Linear Filtering and Correlation
 8.3 A Linear Filtering Approach to Computation of the DFT
 8.3.1 The Goertzel Algorithm
 8.3.2 The Chirpz Transform Algorithm
 8.4 Quantization Effects in the Computation of the DFT
 8.4.1 Quantization Errors in the Direct Computation of the DFT
 8.4.2 Quantization Errors in FFT Algorithms
 8.5 Summary
 Problems
 Computer Problems
 8.1 Efficient Computation of the DFT: FFT Algorithms
 Implementation of DiscreteTime Systems
 9.1 Structures for the Realization of DiscreteTime Systems
 9.2 Structures for FIR Systems
 9.2.1 DirectForm Structure
 9.2.2 CascadeForm Structures
 9.2.3 FrequencySampling Structures
 9.2.4 Lattice Structure
 9.3 Structures for IIR Systems
 9.3.1 DirectForm Structures
 9.3.2 Signal Flow Graphs and Transposed Structures
 9.3.3 CascadeForm Structures
 9.3.4 ParallelForm Structures
 9.3.5 Lattice and LatticeLadder Structures for IIR Systems
 9.4 Representation of Numbers
 9.4.1 FixedPoint Representation of Numbers
 9.4.2 Binary FloatingPoint Representation of Numbers
 9.4.3 Errors Resulting from Rounding and Truncation
 9.5 Quantization of Filter Coefficients
 9.5.1 Analysis of Sensitivity to Quantization of Filter Coefficients
 9.5.2 Quantization of Coefficients in FIR Filters
 9.6 RoundOff Effects in Digital Filters
 9.6.1 LimitCycle Oscillations in Recursive Systems
 9.6.2 Scaling to Prevent Overflow
 9.6.3 Statistical Characterization of Quantization Effects in FixedPoint Realizations of Digital Filters
 9.7 Summary
 Problems
 Computer Problems
 Design of Digital Filters
 10.1 General Considerations
 10.1.1 Causality and Its Implications
 10.1.2 Characteristics of Practical FrequencySelective Filters
 10.2 Design of FIR Filters
 10.2.1 Symmetric and Antisymmetric FIR Filters
 10.2.2 Design of LinearPhase FIR Filters Using Windows
 10.2.3 Design of LinearPhase FIR Filters by the FrequencySampling Method
 10.2.4 Design of Optimum Equiripple LinearPhase FIR Filters
 10.2.5 Design of FIR Differentiators
 10.2.6 Design of Hilbert Transformers
 10.2.7 Comparison of Design Methods for LinearPhase FIR Filters
 10.3 Design of IIR Filters From Analog Filters
 10.3.1 IIR Filter Design by Approximation of Derivatives
 10.3.2 IIR Filter Design by Impulse Invariance
 10.3.3 IIR Filter Design by the Bilinear Transformation
 10.3.4 Characteristics of Commonly Used Analog Filters
 10.3.5 Some Examples of Digital Filter Designs Based on the Bilinear Transformation
 10.4 Frequency Transformations
 10.4.1 Frequency Transformations in the Analog Domain
 10.4.2 Frequency Transformations in the Digital Domain
 10.5 Summary
 Problems
 Computer Problems
 10.1 General Considerations
 Multirate Digital Signal Processing
 11.1 Introduction
 11.2 Decimation by a Factor D
 11.3 Interpolation by a Factor I
 11.4 Sampling Rate Conversion by a Rational Factor I /D
 11.5 Implementation of Sampling Rate Conversion
 11.5.1 Polyphase Filter Structures
 11.5.2 Interchange of Filters and Downsamplers/Upsamplers
 11.5.3 Sampling Rate Conversion with Cascaded Integrator Comb Filters
 11.5.4 Polyphase Structures for Decimation and Interpolation Filters
 11.5.5 Structures for Rational Sampling Rate Conversion
 11.6 Multistage Implementation of Sampling Rate Conversion
 11.7 Sampling Rate Conversion of Bandpass Signals
 11.8 Sampling Rate Conversion by an Arbitrary Factor
 11.8.1 Arbitrary Resampling with Polyphase Interpolators
 11.8.2 Arbitrary Resampling with Farrow Filter Structures
 11.9 Applications of Multirate Signal Processing
 11.9.1 Design of Phase Shifters
 11.9.2 Interfacing of Digital Systems with Different Sampling Rates
 11.9.3 Implementation of Narrowband Lowpass Filters
 11.9.4 Subband Coding of Speech Signals
 11.10 Summary
 Problems
 Computer Problems
 Multirate Digital Filter Banks and Wavelets
 12.1 Multirate Digital Filter Banks
 12.1.1 DFT Filter Banks
 12.1.2 Polyphase Structure of the Uniform DFT Filter Bank
 12.1.3 An Alternative Structure of the Uniform DFT Filter Bank
 12.2 TwoChannel Quadrature Mirror Filter Bank
 12.2.1 Elimination of Aliasing
 12.2.2 Polyphase Structure of the QMF Bank
 12.2.3 Condition for Perfect Reconstruction
 12.2.4 Linear Phase FIR QMF Bank
 12.2.5 IIR QMF Bank
 12.2.6 Perfect Reconstruction in TwoChannel FIR QMF Bank
 12.2.7 TwoChannel Paraunitary QMF Bank
 12.2.8 Orthogonal and Biorthogonal Twochannel FIR Filter Banks
 12.2.9 TwoChannel QMF Banks in Subband Coding
 12.3 MChannel Filter Banks
 12.3.1 Polyphase Structure for the MChannel Filter Bank
 12.3.2 MChannel Paraunitary Filter Banks
 12.4 Wavelets and Wavelet Transforms
 12.4.1 Ideal Bandpass Wavelet Decomposition
 12.4.2 Signal Spaces and Wavelets
 12.4.3 Multiresolution Analysis and Wavelets
 12.4.4 The Discrete Wavelet Transform
 12.5 From Wavelets to Filter Banks
 12.5.1 Dilation Equations
 12.5.2 Orthogonality Conditions
 12.5.3 Implications of Orthogonality and Dilation Equations
 12.6 From Filter Banks to Wavelets
 12.7 Regular Filters and Wavelets
 12.8 Summary
 Problems
 Computer Problems
 12.1 Multirate Digital Filter Banks
 Linear Prediction and Optimum Linear Filters
 13.1 Random Signals, Correlation Functions, and Power Spectra
 13.1.1 Random Processes
 13.1.2 Stationary Random Processes
 13.1.3 Statistical (Ensemble) Averages
 13.1.4 Statistical Averages for Joint Random Processes
 13.1.5 Power Density Spectrum
 13.1.6 DiscreteTime Random Signals
 13.1.7 Time Averages for a DiscreteTime Random Process
 13.1.8 MeanErgodic Process
 13.1.9 CorrelationErgodic Processes
 13.1.10 Correlation Functions and Power Spectra for Random Input Signals to LTI Systems
 13.2 Innovations Representation of a Stationary Random Process
 13.2.1 Rational Power Spectra
 13.2.2 Relationships Between the Filter Parameters and the Autocorrelation Sequence
 13.3 Forward and Backward Linear Prediction
 13.3.1 Forward Linear Prediction
 13.3.2 Backward Linear Prediction
 13.3.3 The Optimum Reflection Coefficients for the Lattice Forward and Backward Predictors
 13.3.4 Relationship of an AR Process to Linear Prediction
 13.4 Solution of the Normal Equations
 13.4.1 The Levinson—Durbin Algorithm
 13.5 Properties of the Linear PredictionError Filters
 13.6 AR Lattice and ARMA LatticeLadder Filters
 13.6.1 AR Lattice Structure
 13.6.2 ARMA Processes and LatticeLadder Filters
 13.7 Wiener Filters for Filtering and Prediction
 13.7.1 FIR Wiener Filter
 13.7.2 Orthogonality Principle in Linear MeanSquare Estimation
 13.7.3 IIR Wiener Filter
 13.7.4 Noncausal Wiener Filter
 13.8 Summary
 Problems
 Computer Problems
 13.1 Random Signals, Correlation Functions, and Power Spectra
 Adaptive Filters
 14.1 Applications of Adaptive Filters
 14.1.1 System Identification or System Modeling
 14.1.2 Adaptive Channel Equalization
 14.1.3 Suppression of Narrowband Interference in a Wideband Signal
 14.1.4 Adaptive Line Enhancer
 14.1.5 Adaptive Noise Cancelling
 14.1.6 Adaptive Arrays
 14.2 Adaptive DirectForm FIR Filters  The LMS Algorithm
 14.2.1 Minimum MeanSquareError Criterion
 14.2.2 The LMS Algorithm
 14.2.3 Related Stochastic Gradient Algorithms
 14.2.4 Properties of the LMS Algorithm
 14.3 Adaptive DirectForm Filters  RLS Algorithms
 14.3.1 RLS Algorithm
 14.3.2 The LDU Factorization and SquareRoot Algorithms
 14.3.3 Fast RLS Algorithms
 14.3.4 Properties of the DirectForm RLS Algorithms
 14.4 Adaptive LatticeLadder Filters
 14.4.1 Recursive LeastSquares LatticeLadder Algorithms
 14.4.2 Other Lattice Algorithms
 14.4.3 Properties of LatticeLadder Algorithms
 14.5 Stability and Robustness of Adaptive Filter Algorithms
 14.6 Summary
 Problems
 Computer Problems
 14.1 Applications of Adaptive Filters
 Power Spectrum Estimation
 15.1 Estimation of Spectra from FiniteDuration Observations of Signals
 15.1.1 Computation of the Energy Density Spectrum
 15.1.2 Estimation of the Autocorrelation and Power Spectrum of Random Signals: The Periodogram
 15.1.3 The Use of the DFT in Power Spectrum Estimation
 15.2 Nonparametric Methods for Power Spectrum Estimation
 15.2.1 The Bartlett Method: Averaging Periodograms
 15.2.2 The Welch Method: Averaging Modified Periodograms
 15.2.3 The Blackman and Tukey Method: Smoothing the Periodogram
 15.2.4 Performance Characteristics of Nonparametric Power Spectrum Estimators
 15.2.5 Computational Requirements of Nonparametric Power Spectrum Estimates
 15.3 Parametric Methods for Power Spectrum Estimation
 15.3.1 Relationships Between the Autocorrelation and the Model Parameters
 15.3.2 The Yule—Walker Method for the AR Model Parameters
 15.3.3 The Burg Method for the AR Model Parameters
 15.3.4 Unconstrained LeastSquares Method for the AR Model Parameters
 15.3.5 Sequential Estimation Methods for the AR Model Parameters
 15.3.6 Selection of AR Model Order
 15.3.7 MA Model for Power Spectrum Estimation
 15.3.8 ARMA Model for Power Spectrum Estimation
 15.3.9 Some Experimental Results
 15.4 ARMA Model Parameter Estimation
 15.5 Filter Bank Methods
 15.5.1 Filter Bank Realization of the Periodogram
 15.5.2 Minimum Variance Spectral Estimates
 15.6 Eigenanalysis Algorithms for Spectrum Estimation
 15.6.1 Pisarenko Harmonic Decomposition Method
 15.6.2 Eigendecomposition of the Autocorrelation Matrix for Sinusoids in White Noise
 15.6.3 MUSIC Algorithm
 15.6.4 ESPRIT Algorithm
 15.6.5 Order Selection Criteria
 15.6.6 Experimental Results
 15.7 Summary
 Problems
 Computer Problems
 Random Number Generators
 Tables of Transition Coefficients for the Design of LinearPhase FIR Filters
 15.1 Estimation of Spectra from FiniteDuration Observations of Signals
References and Bibliography
Answers to Selected Problems
Index
Your questions answered
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