Book Name: Digital
Signal Processing – Principles, Algorithms & Applications
Author: John G. Proakis & Dimitris G.Manolakis
Pages: 1103
Edition:Fourth
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Contents
Preface
1
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
Continuous-Time Versus Discrete-TIme Signals
1.2.3
Continuous-Valued Versus Discrete-Valued Signals
1.2.4
Deterministic Versus Random Signals
1.3 The Concept of
Frequency in Continuous-Time and Discrete-Time Signals
1.3.1
Continuous-Time Sinusoidal Signals
1.3.2
Discrete-Time Sinusoidal Signals
1.3.3 Harmonically
Related Complex Exponentials
1.4
Analog-to-Digital and Digital-to-Analog Conversion
1.4.1 Sampling of
Analog Signals
1.4.2 The 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 Signals and Systems Versus Discrete-Time Signals
and Systems
1.5 Summary and
References
Problems
2 Discrete-Time
Signals and 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-Time 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 the Analysis of Linear Systems
2.3.2 Resolution
of a Discrete-Time 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 Time-Invariant Systems
2.3.6 Stability of
Linear Time-Invariant System
2.3.7 Systems with
Finite-Duration and Infinite-Duration Impulse
Response
2.4 Discrete-Time
Systems Described by Difference Equations
2.4.1 Recursive
and Nonrecursive Discrete-Time Systems
2.4.2 Linear
Time-Invariant Systems Characterized by
Constant-Coefficient
Difference Equations
2.4.3 Solution of
Linear Constant-Coefficient Difference Equations
2.4.4 The Impulse
Response of a Linear Time-Invariant Recursive System
2.5 Implementation
of Discrete-Time Systems
2.5.1 Structures
for the Realization of Linear Time-Invariant Systems
2.5.2 Recursive
and Nonrecursive Realizations of FIR Systems
2.6 Correlation of
Discrete-Time Signal
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 Input-Output
Correlation Sequences
2.7 Summary and
References
Problems
3 The z
-Transform and Its Application to the Analysis of L TI
Systems
3.1 The
z-Transform
3.1.1 The Direct
z-Transform
3.1.2 The Inverse
z-Transform
3.2 Properties of
the z-Transform
3.3 Rational
z-Transforms
3.3.1 Poles and
Zeros
3.3.2 Pole
Location and TIme-Domain Behavior for Causal Signals
3.3.3 The System
Function of a Linear Time-Invariant System
3.4 Inversion of
the z-Transform
3.4.1 The Inverse
z-Transform by Contour Integration
3.4.2 The Inverse
z-Transform by Power Series Expansion
3.4.3 The Inverse
z-Transform by Partial-Fraction Expansion
3.4.4
Decomposition of Rational z-Transforms
3.5 Analysis of
Linear Time-Invariant Systems in the z-Domain
3.5.1 Response of
Systems with Rational System Functions
3.5.2 Transient
and Steady-State Responses
3.5.3 Causality
and Stability
3.5.4 Pole-Zero
Cancellations
3.5.5
Multiple-Order Poles and Stability
3.5.6 Stability of
Second-Order Systems
3.6 The One-sided
z-Transform
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 and
References
Problems
4 Frequency
Analysis of Signals
4.1 Frequency
Analysis of Continuous-Time Signals
4.1.1 The Fourier
Series for Continuous-TIme Periodic Signals
4.1.2 Power
Density Spectrum of Periodic Signals
4.1.3 The 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 The Fourier
Series for Discrete-TIme Periodic Signals
4.2.2 Power
Density Spectrum of Periodic Signals
4.2.3 The fourier
Transform of Discrete-TIme Aperiodic Signals
4.2.4 Convergence
of the Fourier Transform
4.2.5 Energy
Density Spectrum of Aperiodk Signals
4.2.6 Relationship
of the Fourier Transform to the z -Transform
4.2.7 The Cepstrum
4.2.8 The Fourier
Transform of Signals with Poles on the Unit Circle
4.2.9
Frequency-Domain Classification of Signals: The Concept of
Bandwidth
4.2.10 The
Frequency Ranges of Some Natural Signals
4.3 Frequency-Domain
and Time-Domain Signal Properties
4.4 Properties of
the Fourier Transform for Discrete-Time Signals
4.4.1 Symmetry
Properties of the Fourier Transform
4.4.2 Fourier
Transform Theorems and Properties
4.5 Summary and
References
Problems
5 Frequency-Domain
Analysis of LTI Systems
5.1
Frequency-Domain Characteristics of Linear TIme-Invariant Systems
5.1.1 Response to
Complex Exponential and Sinusoidal Signals: The
Frequency Response
Function
5.1.2 Steady-State
and Transient Response to Sinusoidal Input Signals
5.1.3 Steady-State
Response to Periodic Input Signals
5.1.4 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
5.3.1 Input-Output
Correlation Functions and Spectra
5.3.2 Correlation
Functions and Power Spectra for Random Input Signals
5.4 Linear
Time-Invariant Systems as Frequency-Selective 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 All-Pass
Filters
5.4.7 Digital
Sinusoidal Oscillators
5.5 Inverse
Systems and Deconvolution
5.5.1
Invertibility of Linear Time-Invariant Systems
5.5.2
Minimum-Phase, Maximum-Phase, and Mixed-Phase Systems
5.5.3 System
Identification and Deconvolution
5.5.4 -
Homomorphic Deconvolution
5.6 Summary and
References
Problems
6 Sampling and
Reconstruction of Signals
6.1 Ideal Sampling
and Reconstruction of Continuous-Time Signals
6.2 Discrete-Time
Processing of Continuous-Time Signals
6.3
Analog-to-Digital and Digital-to-Analog Converters
6.3.1
Analog-to-Digital Converters
6.3.2 Quantization
and Coding
6.3.3 Analysis of
Quantization Errors
6.3.4
Digital-to-Analog Converters
6.4 Sampling and
Reconstruction of Continuous-Time Bandpass Signals
6.4.1 Uniform or
First-Order Sampling
6.4.2 Interleaved
or Nonuniform Second-Order Sampling
6.4.3 Bandpass
Signal Representations
6.4.4 Sampling
Using Bandpass Signal Representations
6.5 Sampling of
Discrete-Time Signals
6.5.1 Sampling and
Interpolation of Discrete-Time Signals
6.5.2
Representation and Sampling of Bandpass Discrete-Time Signals
6.6 Oversampling
A/D and D/ A Converters
6.6.1 Oversampling
AID Converters
6.6.2 Oversampling
DI A Converters
6.7 Summary and
References
Problems
7 The Discrete
Fourier Transform: Its Properties and Applications
7.1
Frequency-Domain Sampling: The Discrete Fourier Transform
7.1.1
Frequency-Domain Sampling and Reconstruction of Discrete-Time
Signals
7.1.2 The Discrete
Fourier Transform (OFT)
7.1.3 The DFT as a
Linear Transformation
7.1.4 Relationship
of the DFT to Other Transforms
7.2 Properties of
the OFT
7.2.1 Periodicity,
Linearity, and Symmetry Properties
7.2.2
Multiplication of Two DFTs and Circular Convolution
7.2.3 Additional
OFT Properties
7.3 Linear
Filtering Methods Based on the OFT
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 OFT
7.5 The Discrete
Cosine Transform
7.5.1 Forward DCT
7.5.2 Inverse DCT
7.5.3 DCT as an
Orthogonal Transform
7.6 Summary and
References
Problems
8 Efficient
Computation of the DFT: Fast Fourier Transform
Algorithms
8.1 Efficient
Computation of the OFT: FFT Algorithms
8.1.1 Direct
Computation of the DFT
8.1.2
Oivide-and-Conquer Approach to Computation of the DFT
8.1.3 Radix-2 FFT
Algorithms
8.1.4 Radix-4 FFT
Algorithms
8.1.5 Split-Radix
FFT Algorithms
8.1.6
Implementation of FFT Algorithms
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 2N -Point 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 Chirp-z
Transform Algorithm
8.4 Quantization
Effects in the Computation of the DFT
8.4.1 Quantization
Errors in the Direct Computation of the Off
8.4.2 Quantization
Errors in FFT Algorithms
8.5 Summary and
References
Problems
9
Implementation of Discrete-Time Systems
9.1 Structures for
the Realization of Discrete-Time Systems
9.2 Structures for
FIR Systems
9.2.1 Direct-Form
Structure
9.2.2 Cascade-Form
Structures
9.2.3
Frequency-Sampling Structures
9.2.4 Lattice
Structure
9.3 Structures for
IIR Systems
9.3.1 Direct-Form
Structures
9.3.2 Signal Flow
Graphs and Transposed Structures
9.3.3 Cascade-Form
Structures
9.3.4
Parallel-Form Structures
9.3.5 Lattice and
Lattice-Ladder Structures for IIR Systems
9.4 Representation
of Numbers
9.4.1 Fixed-Point
Representation of Numbers
9.4.2 Binary
Floating-Point 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 Round-Off
Effects in Digital Filters
9.6.1 Limit-Cycle
Oscillations in Recursive Systems
9.6.2 Scaling to
Prevent Overflow
9.6.3 Statistical
Characterization of Quantization Effects in Fixed-Point
Realizations of
Digital Filters
9.7 Summary and
References
Problems
1 0 Design of
Digital Filters
10.1 General
Considerations
10.1.1 Causality
and Its Implications
10.1.2
Characteristics of Practical Frequency-Selective Filters
10.2 Design of FIR
Filters
10.2.1 Symmetric
and Antisymmetric FIR Filters
10.2.2 Design of
Linear-Phase FIR Filters Using Windows
10.2.3 Design of
Linear-Phase FIR Filters by the Frequency-Sampling
Method
10.2.4 Design of
Optimum Equiripple Linear-Phase FIR Filters
10.2.5 Design of
FIR Differentiators
10.2.6 Design of
Hilbert Transformers
10.2.7 Comparison
of Design Methods for Linear-Phase FIR Filters
10.3 Design of IIR
Filters From Analog Filters
10.3.1 JIR 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 and
References
Problems
11 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 1/ D
11.5
Implementation of Sampling Rate Conversion
11.5.1 Polyphase
Filter Structures
11.5.2 Interchange
of Filters and Downsamp\ers/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 Digital
Filter Banks
11.10.1 Polyphase
Structures of Uniform Filter Banks
11.10.2
Transmultiplexers
11.11 Two-Channel
Quadrature Mirror Filter Bank
11.11.1
Elimination of Aliasing
11.11.2 Condition
for Perfect Reconstruction
11.11.3 Polyphase
Form of the QMF Bank
11.11.4 Linear
Phase FIR QMF Bank
11.11.5 IIR QMF
Bank
11.11.6 Perfect
Reconstruction Two-Channel FIR QMF Bank
11.11.7
Two-Channel QMF Banks in Subband Coding
11.12 M-Channel
QMF Bank
11.12.1 Alias-Free
and Perfect Reconstruction Condition
11.12.2 Polyphase
Form of the M -Channel QMF Bank
11.13 Summary and
References
Problems
12 Linear
Prediction and Optimum Linear Filters
12.1 Random
Signals, Correlation Functions, and Power Spectra
12.1.1 Random
Processes
12.1.2 Stationary
Random Processes
12.1.3 Statistical
(Ensemble) Averages
12.1.4 Statistical
Averages for Joint Random Processes
12.1.5 Power
Density Spectrum
12.1.6
Discrete-Time Random Signals
12.1.7 Time
Averages for a Discrete-TIme Random Process
12.1.8
Mean-Ergodic Process
12.1.9
Correlation-Ergodic Processes
12.2 Innovations
Representation of a Stationary Random Process
12.2.1 Rational
Power Spectra 836
12.2.2
Relationships Between the Filter Parameters and the
Autocorrelation
Sequence
12.3 Forward and
Backward linear Prediction
12.3.1 Forward
Linear Prediction
12.3.2 Backward
Linear Prediction
12.3.3 The Optimum
Reflection Coefficients for the Lattice Forward and
Backward
Predictors
12.3.4
Relationship of an AR Process to Linear Prediction
12.4 Solution of
the Normal Equations
12.4.1 The
Levinson-Durbin Algorithm
12.4.2 The Schur
Algorithm
12.5 Properties of
the linear Prediction-Error Filters
12.6 AR Lattice
and ARMA Lattice-Ladder Filters
12.6.1 AR Lattice
Structure
12.6.2 ARMA
Processes and Lattice-Ladder Filters
12.7 Wiener
Filters for Filtering and Prediction
12.7.1 FIR Wiener
Filter
12.7.2
Orthogonality Principle in Linear Mean-Square Estimation
12.7.3 IIR Wiener
Filter
12.7.4 Noncausal
Wiener Filter
12.8 Summary and
References
Problems
1 3 Adaptive
Filter
13.1 Applications
of Adaptive Filters
13.1.1 System
Identification or System Modeling
13.1.2 Adaptive
Channel Equalization
13.1.3 Echo
Cancellation in Data Transmission over Telephone Channels
13.1.4 Suppression
of Narrowband Interference in a Wideband Signal
13.1.5 Adaptive
Line Enhancer
13.1.6 Adaptive
Noise Cancelling
13.1.7 Linear
Predictive Coding of Speech Signals
13.1.8 Adaptive
Arrays
13.2 Adaptive
Direct-Form FIR Filters-The LMS Algorithm
13.2.1 Minimum
Mean-Square-Error Criterion
13.2.2 The LMS
Algorithm
13.2.3 Related
Stochastic Gradient Algorithms
13.2.4 Properties
of the LMS Algorithm
13.3 Adaptive
Direct-Form Filters-RLS Algorithms
13.3.1 RLS
Algorithm
13.3.2 The LOU
Factorization and Square-Root Algorithms
13.3.3 Fast RLS
Algorithms
13.3.4 Properties
of the Direct-Form RLS Algorithms
13.4 Adaptive
Lattice-Ladder Filters
13.4.1 Recursive
Least-Squares Lattice-Ladder Algorithms
13.4.2 Other
Lattice Algorithms
13.4.3 Properties
of Lattice-Ladder Algorithms
13.5 Summary and
References
Problems
14 Power
Spectrum Estimation
14.1 Estimation of
Spectra from Finite-Duration Observations of Signals
14.1.1 Computation
of the Energy Density Spectrum
14.1.2 Estimation
of the Autocorrelation and Power Spectrum of Random
Signals: The
Periodogram
14.1.3 The Use of
the OFT in Power Spectrum Estimation
14.2 Nonparametric
Methods for Power Spectrum Estimation
14.2.1 The
Bartlett Method: Averaging Periodograms
14.2.2 The Welch
Method: Averaging Modified Periodograms
14.2.3 The
Blackman and Tukey Method: Smoothing the Periodogram
14.2.4 Performance
Characteristics of Nonparametric Power Spectrum
Estimators
14.2.5
Computational Requirements of Nonparametric Power Spectrum
Estimates
14.3 Parametric
Methods for Power Spectrum Estimation
14.3.1
Relationships Between the Autocorrelation and the Model
Parameters
14.3.2 The
Yule-Walker Method for the AR Model Parameters
14.3.3 The Burg
Method for the AR Model Parameters
14.3.4
Unconstrained Least-Squares Method for the AR Model
Parameters
14.3.5 Sequential
Estimation Methods for the AR Model Parameters
14.3.6 Selection
of AR Model Order
14.3.7 MA Model
for Power Spectrum Estimation
14.3.8 ARMA Model
for Power Spectrum Estimation
14.3.9 Some
Experimental Results
14.4 Filter Bank
Methods
14.4.1 Filter Bank
Realization of the Periodogram
14.4.2 Minimum
Variance Spectral Estimates
14.5 Eigenanalysis
Algorithms for Spectrum Estimation
14.5.1 Pisarenko
Harmonic Decomposition Method
14.5.2
Eigen-decomposition of the Autocorrelation Matrix for Sinusoids in
White Noise
14.5.3 MUSIC
Algorithm
14.5.4 ESPRIT
Algorithm
14.5.5 Order
Selection Criteria
14.5.6
Experimental Results
14.6 Summary and
References
Problem
A Random Number
Generators
B Tables of
Transition Coefficients for the Design of Linear-Phase
FIR Filters
References and
Bibliography
Answers to
Selected Problems
Index
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