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Digital Signal Processing – Principles, Algorithms & Applications by John G. Proakis & Dimitris G.Manolakis



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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