Digital Signal Processing

Digital Signal Processing: Principles, Algorithms & Applications (3rd Ed.)
Copyright
Contents
Preface
Ch1 Introduction
1.1 Signals, Systems & Signal Processing
1.1.1 Basic Elements of DSP System
1.1.2 Advantages of Digital over Analog Signal
Processing
1.2 Classification of Signals
1.2.1 Multichannel & Multidimensional Signals
1.2.2 Continuous-Time vs Discrete-Time Signals
1.2.3 Continuous-Valued vs Discrete-Valued Signals
1.2.4 Deterministic vs Random Signals
1.3 Concept of Frequency in Continuous-Time & Discrete-Time Signals
1.3.1 Continuous-Time Sinusoidal Signals
1.3.2 Discrete-Time Sinusoidat Signals
1.3.3 Harmonically Related Complex Exponentiais
1.4 Analog-to-Digital & Digital-to-Analog Conversion
1.4.1 Sampling of Analog Signals
1.4.2 Sampling Theorem
1.4.3 Quantization of Continuous-Amplitude Signals
1.4.4 Quantization of Sinusoidal Signals
1.4.5 Coding of Quantized Samples
1.4.6 Digital-to-Analog Conversion
1.4.7 Analysis of Digital Signats & Systems vs Discrete-Time Signals & Systems
1.5 Summary & References
Problems
Ch2 Discrete-Time Signals & Systems
2.1 Discrete-Time Signals
2.1.1 Some Elementary Discrete-Time Signals
2.1.2 Classification of Discrete-Time Signals
2.1.3 Simple Manipulations of Discrete-Time Signals
2.2 Discrete-Time Systems
2.2.1 Input-Output Description of Systems
2.2.2 Block Diagram Representation of Discrete-Tlme
Systems
2.2.3 Classification of Discrete-Time Systems
2.2.4 Interconnection of Discrete-Time Systems
2.3 Analysis of Discrete-Time Linear Time-Invariant Systems
2.3.1 Techniques for Analysis of Linear Systems
2.3.2 Resolution of Discrete-Time Signal into Impulses
2.3.3 Response of LTI Systems to Arbitrary Inputs: Convolution Sum
2.3.4 Properties of Convolution & Interconnection of LTI Systems
2.3.5 Causal Linear Time-Invariant Systems
2.3.6 Stability of Linear Time-invariant Systems
2.3.7 Systems with Finite-Duration & Infinite-Duration Impulse Response
2.4 Discrete-Time Systems described by Difference Equations
2.4.1 Recursive & Nonrecursive Discrete-Time Systems
2.4.2 Linear Time-Invariant Systems characterized by Constant-Coefficient Difference Equation
2.4.3 Solution of Linear Constant-Coefficient Difference Equations
2.4.4 Impulse Response of Linear Time-Invariant Recursive System
2.5 Implementation of Discrete-Time Systems
2.5.1 Structures for Realization of Linear Time-Invariant Systems
2.5.2 Recursive & Nonrecursive Realizations of FIR Systems
2.6 Correlation of Discrete-Time Signals
2.6.1 Crosscorrelation & Autocorretation Sequences
2.6.2 Properties of Autocorrelation & Crosscorrelation Sequences
2.6.3 Correlation of Periodic Sequences
2.6.4 Computation of Correlation Sequences
2.6.5 Input-Output Correlation Sequences
2.7 Summary & References
Problems
Ch3 z-Transform & its Application to Analysis of LTI Systems
3.1 z-Transform
3.1.1 Direct z-Transform
3.1.2 Inverse z-Transform
3.2 Properties of z-Transform
3.3 Rational z -Transforms
3.3.1 Poles & Zeros
3.3.2 Pole Location & Time-Domain Behavior for Causal Signals
3.3.3 System Function of Linear Tirne-Invariant System
3.4 Inversion of z-Transform
3.4.1 Inverse z-Transform by Contour Integration
3.4.2 Inverse z-Transform by Power Series Expansion
3.4.3 Inverse z-Transform by Partial-Fraction Expansion
3.4.4 Decomposition of Rational z-Transforms
3.5 One-Sided z-Transform
3.5.1 Definition & Properties
3.5.2 Solution of Difference Equations
3.6 Analysis of Linear Time-Invariant Systems in z-Domain
3.6.1 Response of Systems with Rational System
Functions
3.6.2 Response of Pole-Zero Systems with Nonzero
Initial Conditions
3.6.3 Transient & Steady-State Responses
3.6.4 Causality & Stability
3.6.5 Pole-Zero Cancellations
3.6.6 Multiple-Order Poles & Stability
3.6.7 Schur-Cohn Stability Test
3.6.8 Stability of Second-Order Systems
3.7 Summary & References
Problems
Ch4 Frequency Analysis of Signals & Systems
4.1 Frequency Analysis of Continuous-Time Signals
4.1.1 Fourier Series for Continuous-Time Periodic Signals
4.1.2 Power Density Spectrum of Periodic Signals
4.1.3 Fourier Transform for Continuous-Time Aperiodic Signals
4.1.4 Energy Density Spectrum of Aperiodic Signals
4.2 Frequency Analysis of Discrete-Time Signals
4.2.1 Fourier Series for Discrete-Time Periodic Signals
4.2.2 Power Density Spectrum of Periodic Signals
4.2.3 Fourier Transform of Discrete-Time Aperiodic Signals
4.2.4 Convergence of Fourier Transform
4.2.5 Energy Density Spectrum of Aperiodic Signals
4.2.6 Relationship of Fourier Transform to z-Transform
4.2.7 Cepstrum
4.2.8 Fourier Transform of Signals with Poles on Unit Circle
4.2.9 Sampling Theorem Revisited
4.2.10 Frequency-Domain Classification of Signals: Concept of Bandwidth
4.2.11 Frequency Ranges of Some Natural Signals
4.2.12 Physical & Mathematical Dualities
4.3 Properties of Fourier Transform for Discrete-Time Signals
4.3.1 Symmetry Properties of Fourier Transform
4.3.2 Fourier Transform Theorems & Properties
4.4 Frequency-Domain Characteristics of LTI Systems
4.4.1 Response to Complex Exponential & Sinusoidal Signals: Frequency Response Function
4.4.2 Steady-State & Transient Response to Sinusoidal Input Signals
4.4.3 Steady-State Response to Periodic Input Signals
4.4.4 Response to Aperiodic Input Signals
4.4.5 Relationships between System Function & Frequency Response Function
4.4.6 Computation of Frequency Response Function
4.4.7 Input-Output Correlation Functions & Spectra
4.4.8 Correlation Functions & Power Spectra for Random Input Signals
4.5 LTI Systems as Frequency-Selective Filters
4.5.1 Ideal Filter Characteristics
4.5.2 Lowpass, Highpass & Bandpass Filters
4.5.3 Digital Resonators
4.5.4 Notch Filters
4.5.5 Comb Filters
4.5.6 All-Pass Filters
4.5.7 Digital Sinusoidal Oscillators
4.6 Inverse Systems & Deconvolution
4.6.1 lnvertibility of LTI Systems
4.6.2 Minimum-Phase, Maximum-Phase & Mixed-Phase Systems
4.6.3 System Identification & Deconvolution
4.6.4 Homomorphic Deconvolution
4.7 Summary & References
Problems
Ch5 Discrete Fourier Transform: its Properties & Applications
5.1 Frequency Domain Sampling: DFT
5.1.1 Frequency-Domain Sampling & Reconstruction of Discrete-Time Signals
5.1.2 Discrete Fourier Transform (DFT)
5.1.3 DFT as Linear Transformation
5.1.4 Relationship of DFT to other Transforms
5.2 Properties of DFT
5.2.1 Periodicity, Linearity & Symmetry Properties
5.2.2 Multiplication of 2 DFTs & Circular Convolution
5.2.3 Additional DFT Properties
5.3 Linear Filtering Methods based on DFT
5.3.1 Use of DFT in Linear Filtering
5.3.2 Filtering of Long Data Sequences
5.4 Frequency Analysis of Signals using DFT
5.5 Summary & References
Problems
Ch6 Efficient Computation of DFT: Fast Fourier Transform Algorithms
6.1 Efnclent Computation of DFT: FFT Algorithms
6.1.1 Direct Computation of DFT
6.1.2 Divide-&-Conquer Approach to Computation of DFT
6.1.3 Radix-2 FFT Algorithms
6.1.4 Radix-4 FFT Algorithms
6.1.5 Split-Radix FFT Algorithms
6.1.6 Implementation of FFT Algorithms
6.2 Applications of FFT Algorrhms
6.2.1 Efficient Computation of DTT of 2 Real Sequences
6.2.2 Efficient Computation of DFT of 2N-Point Real Sequence
6.2.3 Use of FFT Algorithm in Linear Filtering & Correlation
6.3 Linear Filtering Approach to Computation of DFT
6.3.1 Goertzel Algorithm
6.3.2 Chirp-z Transform Algorithm
6.4 Quantization Effects in Computation of DFT
6.4.1 Quantization Errors in Direct Computation of DFT
6.4.2 Quantization Errors in FFT Algorithms
6.5 Summary & References
Problems
Ch7 Implementation of Discrete-Time Systems
7.1 Structures for Realization Of Discrete-Time Systems
7.2 Structures for FIR Systems
7.2.1 Direct-Form Structure
7.2.2 Cascade-Form Structures
7.2.3 Frequency-Sampling Structures
7.2.4 Lattice Structure
7.3 Structures for IIR Systems
7.3.1 Direct-Form Structures
7.3.2 Signal Flow Graphs & Transposed Structures
7.3.3 Cascade-Form Structures
7.3.4 Parallel-Form Structures
7.3.5 Lattice & Lattice-Ladder Structures for IIR Systems
7.4 State-Space System Analysis & Structures
7.4.1 State-Space Descriptions of Systems characterized by Difference Equations
7.4.2 Solution of State-Space Equations
7.4.3 Relationships between Input-Output & State-Space Descriptions
7.4.4 State-Space Analysis in z-Domain
7.4.5 Additional State-Space Structures
7.5 Representation of Numbers
7.5.1 Fixed-Point Representation of Numbers
7.5.2 Binary Floating-Point Representation of Numbers
7.5.3 Errors Resulting from Rounding & Truncation
7.6 Quantization of Filter Coefficients
7.6.1 Analysis of Sensitivity to Quantization of Filter
Coefficients
7.6.2 Quantization of Coefficients in FIR Filters
7.7 Round-Off Effects in Digital Filters
7.7.1 Limit-Cycle Oscillations in Recursive Systems
7.7.2 Scaling to Prevent Overflow
7.7.3 Statistical Characterization of Quantization Effects
in Fixed-Point Realizations of Digital Filters
7.8 Summary & References
Problems
Ch8 Design of Digital Filters
8.1 General Considerations
8.1.1 Causality & its Implications
8.1.2 Characteristics of Practical Frequency-Selective Filters
8.2 Design of FIR Filters
8.2.1 Symmetric & Antisymmetric FIR Filters
8.2.2 Design of Linear-Phase FIR Filters using Windows
8.2.3 Design of Linear-Phase FIR Filters by Frequency-Sampling Method
8.2.4 Design of Optimum Equiripple Linear-Phase FIR
Filters
8.2.5 Design of FIR Differentiators
8.2.6 Design of Hilbert Transformers
8.2.7 Comparison of Design Methods for Linear-Phase
FIR Filters
8.3 Design of IIR Fllters from Analog Filters
8.3.1 IIR Filter Design by Approximation of Derivatives
8.3.2 IIR Filter Design by Impulse lnvariance
8.3.3 IIR Filter Design by Bilinear Transformation
8.3.4 Matched-z Transformation
8.3.5 Characteristics of Commonly Used Analog Filters
8.3.6 Some Examples of Digital Filter Designs based on Bilinear Transformation
8.4 Frequency Transformations
8.4.1 Frequency Transformations in Analog Domain
8.4.2 Frequency Transformations in Digital Domain
8.5 Design of Digital Filters based on Least-Squares Method
8.5.1 Pade Approximation Method
8.5.2 Least-Squares Design Methods
8.5.3 FIR Least-Squares Inverse (Wiener) Filters
8.5.4 Design of IIR Filters In Frequency Domain
8.6 Summary & References
Problems
Ch9 Sampling & Reconstruction of Signals
9.1 Sampling of Bandpass Signals
9.1.1 Representation of Bandpass Signals
9.1.2 Sampling of Bandpass Signals
9.1.3 Discrete-Time Processing of Continuous-Time Signals
9.2 Analog-to-Digital Conversion
9.2.1 Sample-and-Hold
9.2.2 Quantization & Coding
9.2.3 Analysis of Quantization Errors
9.2.4 Oversampling A/D Converters
9.3 Digital-to-Analog Conversion
9.3.1 Sample & Hold
9.3.2 First-Order Hold
9.3.3 Linear Interpolation with Delay
9.3.4 Oversampling D/A Converters
9.4 Summary & References
Problems
Ch10 Multirate Digital Signal Processing
10.1 Introduction
10.2 Decimation by Factor D
10.3 Interpolation by Factor I
10.4 Sampling Rate Conversion by Rational Factor 1/D
10.5 Filter Design & Implementation for Sampling-Rate Conversion
10.5.1 Direct-Form FIR Filter Structures
10.5.2 Polyphase Filter Structures
10.5.3 Time-Variant Filter Structures
10.6 Multistage Implementation of Sampling-Rate Converslon
10.7 Sampling-Rate Conversion of Bandpass Signals
10.7.1 Decimation & Interpolation by Frequency Conversion
10.7.2 Modulation-Free Method for Decimation & Interpolation
10.8 Sampling-Rate Conversion by Arbitrary Factor
10.8.1 1st-Order Approximation
10.8.2 2nd-Order Approximation (Linear Interpolation)
10.9 Applicatiows of Multirate Signal Processing
10.9.1 Design of Phase Shifters
10.9.2 Interfacing of Digital Systems with Different
Sampling Rates
10.9.3 Implementation of Narrowband Lowpass Filters
10.9.4 Implementation of Digital Filter Banks
10.9.5 Subband Coding of Speech Signals
10.9.6 Quadrature Mlrror Filters
10.9.7 Transmultiplexers
10.9.8 Oversampling A/D & D/A Conversion
10.10 Summary & References
Problems
Ch11 Linear Prediction & Optimum Linear Filters
11.1 Innovations Representation of Statlonary Random Process
11.1.1 Rational Power Spectra
11.1.2 Relationships between Filter Parameters & Autocorrelation Sequence
11.2 Forward & Backward Linear Prediction
11.2.1 Forward Linear Prediction
11.2.2 Backward Linear Prediction
11.2.3 Optimum Reflection Coefficients for Lattice Forward & Backward Predictors
11.2.4 Relationship of AR Process to Linear Prediction
11.3 Solution of Normal Equations
11.3.1 Levinson-Durbin Algorithm
11.3.2 Schuer Algorithm
11.4 Properties of Linear Prediction-Error Filters
11.5 AR Lattice & ARMA Lattice-Ladder Filters
11.5.1 AR Lattice Structure
11.5.2 ARMA Processes & Lattice-Ladder Filters
11.6 Wiener Filters for Filtering & Prediction
11.6.1 FIR Wiener Filter
11.6.2 Orthogonality Principle in Linear Mean-Square
Estimation
11.6.3 IIR Wiener Filter
11.6.4 Noncausal Wiener Filter
11.7 Summary & References
Problems
Ch12 Power Spectrum Estimation
12.1 Estimation of Spectra from Finite-Duration Observatlons of Signals
12.1.1 Computation of Energy Density Spectrum
12.1.2 Estimation of Autocorrelation & Power Spectrum of Random Signals: Periodogram
12.1.3 Use of DFT in Power Spectrum Estimation
12.2 Nonparametric Methods for Power Spectrum Estimation
12.2.1 Bartlett Method: Averaging Periodograms
12.2.2 Welch Method: Averaging Modified Periodograrns
12.2.3 Blackman & Tukey Method: Smoothing Periodogram
12.2.4 Performance Characteristics of Nonparametric
Power Spectrum Estimators
12.2.5 Computational Requirements of Nonpararnetric
Power Spectrum Estimates
12.3 Parametric Methods for Power Spectrum Estimation
12.3.1 Relationships between Autocorrelation & Model Parameters
12.3.2 Yule-Walker Method for AR Model Parameters
12.3.3 Burg Method for AR Model Parameters
12.3.4 Unconstrained Least-Squares Method for AR Model Parameters
12.3.5 Sequential Estimation Methods for AR Model Parameters
12.3.6 Selection of AR Model Order
12.3.7 MA Model for Power Spectrum Estimation
12.3.8 ARMA Model for Power Spectrum Estimation
12.3.9 Some Experimental Results
12.4 Minimum Variance Spectral Estimation
12.5 Eigenanalysis Algorithms for Spectrum Estimation
12.5.1 Pisarenko Harmonic Decomposition Method
12.5.2 Eigen-Decomposition of Autocorrelation Matrix for Slnusoids in White Noise
12.5.3 MUSIC Algorithm
12.5.4 ESPRIT Algorithm
12.5.5 Order Selection Criteria
12.5.6 Experimental Results
12.6 Summary & References
Problems
AppA Random Signals, Correlation Functions & Power Spectra
Random Processes
Stationary Random Processes
Statistical (Ensemble) Averages
Statistical Averages for Joint Random Processes
Power Density Spectrum
Discrete-Time Random Signals
Time Averages for Discrete-Time Random Process
Mean-Ergodic Process
Correlation-Ergodic Processes
AppB Random Number Generators
AppC Tables of Transition Coefficients for Design of Linear-Phase FIR Filters
AppD List of MatLab Functions
Ch1
Ch2-Ch3
Ch4-Ch7
Ch8
Ch9-Ch10
References & Bibliography
Index