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Electronic Devices and Circuit Theory (11th Edition) by Robert L. Boylestad, Louis Nashelsky
BOOK NAME: Electronic Devices and Circuit Theory
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Electronic devices and circuits By David A. Bell
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Electronic Devices & Circuits-McGraw-Hill (1967) Jacob Millman, Christos C. Halkias Ecerelatedbooks .blogspot.com
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BOOK NAME: Electronic Devices & Circuits-McGraw-Hill (1967)AUTHOR: Jacob Millman, Christos C. HalkiasPAGES: 386
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8086 Microprocessors and its Applications Full Book by A. Nagoor Kani
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Engineering circuit analysis By William H. Hayt, Jack E. Kemmerly, Steven M. Durbin
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Fundamentals of Modern VLSI Devices by Yuan Taur, Tak H. Ning
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Microprocessor and Microcontroller System (Full Book) A. P. Godse Mrs. D. A. Godse
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Signals and Systems Continuous and Discrete (Full Book) by Rodger E. Ziemer, William H Tranter, D. R. Fannin
Book Name:Signals and Systems Continuous and Discrete (Full Book)
Edition: 4th Edition
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Electronic Devices and Circuit Theory by Robert Boylestad Louis Nashelsky (7th Edition) Full Book
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Click Here to DownloadEngineering Electromagnetics by William H. Hayt
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Digital Signal Processing A Computer-Based Approach by Sanjit K. Mitra
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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
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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
Digital Signal Processing A Practical Approach by E.C. Ifeachor, B.W. Jervis
Book Name:Digital Signal Processing A Practical Approach
Author: E.C. Ifeachor, B.W. Jervis
Pages:862Click here to download
Digital Signal Processing SIGNALS SYSTEMS AND FILTERS by Andreas Antoniou
Book Name:Digital Signal Processing SIGNALS SYSTEMS AND FILTERS
Author: Andreas Antoniou
Pages: 991Click here to download
Preface
Chapter 1. Introduction to Digital Signal Processing
1.1 Introduction
1.2 Signals
1.3 Frequency-Domain Representation
1.4 Notation
1.5 Signal Processing
1.6 Analog Filters
1.7 Applications of Analog Filters
1.8 Digital Filters
1.9 Two DSP Applications
1.9.1 Processing of EKG signals
1.9.2 Processing of Stock-Exchange Data
References
Chapter 2. The Fourier Series and Fourier Transform
2.1 Introduction
2.2 Fourier Series
2.2.1 Definition
2.2.2 Particular Forms
2.2.3 Theorems and Properties
2.3 Fourier Transform
2.3.1 Derivation
2.3.2 Particular Forms
2.3.3 Theorems and Properties
References
Problems
Chapter 3. The z Transform
3.1 Introduction
3.2 Definition of z Transform
3.3 Convergence Properties
3.4 The z Transform as a Laurent Series
3.5 Inverse z Transform
3.6 Theorems and Properties
3.7 Elementary Discrete-Time Signals
3.8 z-Transform Inversion Techniques
3.8.1 Use of Binomial Series
3.8.2 Use of Convolution Theorem
3.8.3 Use of Long Division
3.8.4 Use of Initial-Value Theorem
3.8.5 Use of Partial Fractions
3.9 Spectral Representation of Discrete-Time Signals
3.9.1 Frequency Spectrum
3.9.2 Periodicity of Frequency Spectrum
3.9.3 Interrelations
References
Problems
Chapter 4. Discrete-Time Systems
4.1 Introduction
4.2 Basic System Properties
4.2.1 Linearity
4.2.2 Time Invariance
4.2.3 Causality
4.3 Characterization of Discrete-Time Systems
4.3.1 Nonrecursive Systems
4.3.2 Recursive Systems
4.4 Discrete-Time System Networks
4.4.1 Network Analysis
4.4.2 Implementation of Discrete-Time Systems
4.4.3 Signal Flow-Graph Analysis
4.5 Introduction to Time-Domain Analysis
4.6 Convolution Summation
4.6.1 Graphical Interpretation
4.6.2 Alternative Classification
4.7 Stability
4.8 State-Space Representation
4.8.1 Computability
4.8.2 Characterization
4.8.3 Time-Domain Analysis
4.8.4 Applications of State-Space Method
References
Problems
Chapter 5. The Application of the z Transform
5.1 Introduction
5.2 The Discrete-Time Transfer Function
5.2.1 Derivation of H(z) from Difference Equation
5.2.2 Derivation of H(z) from System Network
5.2.3 Derivation of H(z) from State-Space Characterization
5.3 Stability
5.3.1 Constraint on Poles
5.3.2 Constraint on Eigenvalues
5.3.3 Stability Criteria
5.3.4 Test for Common Factors
5.3.5 Schur-Cohn Stability Criterion
5.3.6 Schur-Cohn-Fujiwara Stability Criterion
5.3.7 Jury-Marden Stability Criterion
5.3.8 Lyapunov Stability Criterion
5.4 Time-Domain Analysis
5.5 Frequency-Domain Analysis
5.5.1 Steady-State Sinusoidal Response
5.5.2 Evaluation of Frequency Response
5.5.3 Periodicity of Frequency Response
5.5.4 Aliasing
5.5.5 Frequency Response of Digital Filters
5.6 Transfer Functions for Digital Filters
5.6.1 First-Order Transfer Functions
5.6.2 Second-Order Transfer Functions
5.6.3 Higher-Order Transfer Functions
5.7 Amplitude and Delay Distortion
References
Problems
Chapter 6. The Sampling Process
6.1 Introduction
6.2 Fourier Transform Revisited
6.2.1 Impulse Functions
6.2.2 Periodic Signals
6.2.3 Unit-Step Function
6.2.4 Generalized Functions
6.3 Interrelation Between the Fourier Series and the Fourier Transform
6.4 Poisson’s Summation Formula
6.5 Impulse-Modulated Signals
6.5.1 Interrelation Between the Fourier and z Transforms
6.5.2 Spectral Relationship Between Discrete- and Continuous-Time Signals
6.6 The Sampling Theorem
6.7 Aliasing
6.8 Graphical Representation of Interrelations
6.9 Processing of Continuous-Time Signals Using Digital Filters
6.10 Practical A/D and D/A Converters
References
Problems
Chapter 7. The Discrete Fourier Transform
7.1 Introduction
7.2 Definition
7.3 Inverse DFT
7.4 Properties
7.4.1 Linearity
7.4.2 Periodicity
7.4.3 Symmetry
7.5 Interrelation Between the DFT and the z Transform
7.5.1 Frequency-Domain Sampling Theorem
7.5.2 Time-Domain Aliasing
7.6 Interrelation Between the DFT and the CFT
7.6.1 Time-Domain Aliasing
7.7 Interrelation Between the DFT and the Fourier Series
7.8 Window Technique
7.8.1 Continuous-Time Windows
7.8.2 Discrete-Time Windows
7.8.3 Periodic Discrete-Time Windows
7.8.4 Application of Window Technique
7.9 Simplified Notation
7.10 Periodic Convolutions
7.10.1 Time-Domain Periodic Convolution
7.10.2 Frequency-Domain Periodic Convolution
7.11 Fast Fourier-Transform Algorithms
7.11.1 Decimation-in-Time Algorithm
7.11.2 Decimation-in-Frequency Algorithm
7.11.3 Inverse DFT
7.12 Application of the FFT Approach to Signal Processing
7.12.1 Overlap-and-Add Method
7.12.2 Overlap-and-Save Method
References
Problems
Chapter 8. Realization of Digital Filters
8.1 Introduction
8.2 Realization
8.2.1 Direct Realization
8.2.2 Direct Canonic Realization
8.2.3 State-Space Realization
8.2.4 Lattice Realization
8.2.5 Cascade Realization
8.2.6 Parallel Realization
8.2.7 Transposition
8.3 Implementation
8.3.1 Design Considerations
8.3.2 Systolic Implementations
References
Problems
Chapter 9. Design of Nonrecursive (FIR) Filters
9.1 Introduction
9.2 Properties of Constant-Delay Nonrecursive Filters
9.2.1 Impulse Response Symmetries
9.2.2 Frequency Response
9.2.3 Location of Zeros
9.3 Design Using the Fourier Series
9.4 Use of Window Functions
9.4.1 Rectangular Window
9.4.2 von Hann and Hamming Windows
9.4.3 Blackman Window
9.4.4 Dolph-Chebyshev Window
9.4.5 Kaiser Window
9.4.6 Prescribed Filter Specifications
9.4.7 Other Windows
9.5 Design Based on Numerical-Analysis Formulas
References
Problems
Chapter 10. Approximations for Analog Filters
10.1 Introduction
10.2 Basic Concepts
10.2.1 Characterization
10.2.2 Laplace Transform
10.2.3 The Transfer Function
10.2.4 Time-Domain Response
10.2.5 Frequency-Domain Analysis
10.2.6 Ideal and Practical Filters
10.2.7 Realizability Constraints
10.3 Butterworth Approximation
10.3.1 Derivation
10.3.2 Normalized Transfer Function
10.3.3 Minimum Filter Order
10.4 Chebyshev Approximation
10.4.1 Derivation
10.4.2 Zeros of Loss Function
10.4.3 Normalized Transfer Function
10.4.4 Minimum Filter Order
10.5 Inverse-Chebyshev Approximation
10.5.1 Normalized Transfer Function
10.5.2 Minimum Filter Order
10.6 Elliptic Approximation
10.6.1 Fifth-Order Approximation
10.6.2 Nth-Order Approximation (n Odd)
10.6.3 Zeros and Poles of L(−s2)
10.6.4 Nth-Order Approximation (n Even)
10.6.5 Specification Constraint
10.6.6 Normalized Transfer Function
10.7 Bessel-Thomson Approximation
10.8 Transformations
10.8.1 Lowpass-to-Lowpass Transformation
10.8.2 Lowpass-to-Bandpass Transformation
References
Problems
Chapter 11. Design of Recursive (IIR) Filters
11.1 Introduction
11.2 Realizability Constraints
11.3 Invariant Impulse-Response Method
11.4 Modified Invariant Impulse-Response Method
11.5 Matched-z Transformation Method
11.6 Bilinear-Transformation Method
11.6.1 Derivation
11.6.2 Mapping Properties of Bilinear Transformation
11.6.3 The Warping Effect
11.7 Digital-Filter Transformations
11.7.1 General Transformation
11.7.2 Lowpass-to-Lowpass Transformation
11.7.3 Lowpass-to-Bandstop Transformation
11.7.4 Application
11.8 Comparison Between Recursive and Nonrecursive Designs
References
Problems
Chapter 12. Recursive (IIR) Filters Satisfying Prescribed Specifications
12.1 Introduction
12.2 Design Procedure
12.3 Design Formulas
12.3.1 Lowpass and Highpass Filters
12.3.2 Bandpass and Bandstop Filters
12.3.3 Butterworth Filters
12.3.4 Chebyshev Filters
12.3.5 Inverse-Chebyshev Filters
12.3.6 Elliptic Filters
12.4 Design Using the Formulas and Tables
12.5 Constant Group Delay
12.5.1 Delay Equalization
12.5.2 Zero-Phase Filters
12.6 Amplitude Equalization
References
Problems
Chapter 13. Random Signals
13.1 Introduction
13.2 Random Variables
13.2.1 Probability-Distribution Function
13.2.2 Probability-Density Function
13.2.3 Uniform Probability Density
13.2.4 Gaussian Probability Density
13.2.5 Joint Distributions
13.2.6 Mean Values and Moments
13.3 Random Processes
13.3.1 Notation
13.4 First- and Second-Order Statistics
13.5 Moments and Autocorrelation
13.6 Stationary Processes
13.7 Frequency-Domain Representation
13.8 Discrete-Time Random Processes
13.9 Filtering of Discrete-Time Random Signals
References
Problems
Chapter 14. Effects of FiniteWord Length in Digital Filters
14.1 Introduction
14.2 Number Representation
14.2.1 Binary System
14.2.2 Fixed-Point Arithmetic
14.2.3 Floating-Point Arithmetic
14.2.4 Number Quantization
14.3 Coefficient Quantization
14.4 Low-Sensitivity Structures
14.4.1 Case I
14.4.2 Case II
14.5 Product Quantization
14.6 Signal Scaling
14.6.1 Method A
14.6.2 Method B
14.6.3 Types of Scaling
14.6.4 Application of Scaling
14.7 Minimization of Output Roundoff Noise
14.8 Application of Error-Spectrum Shaping
14.9 Limit-Cycle Oscillations
14.9.1 Quantization Limit Cycles
14.9.2 Overflow Limit Cycles
14.9.3 Elimination of Quantization Limit Cycles
14.9.4 Elimination of Overflow Limit Cycles
References
Problems
Chapter 15. Design of Nonrecursive Filters Using Optimization Methods
15.1 Introduction
15.2 Problem Formulation
15.2.1 Lowpass and Highpass Filters
15.2.2 Bandpass and Bandstop Filters
15.2.3 Alternation Theorem
15.3 Remez Exchange Algorithm
15.3.1 Initialization of Extremals
15.3.2 Location of Maxima of the Error Function
15.3.3 Computation of |E(ω)| and Pc(ω)
15.3.4 Rejection of Superfluous Potential Extremals
15.3.5 Computation of Impulse Response
15.4 Improved Search Methods
15.4.1 Selective Step-by-Step Search
15.4.2 Cubic Interpolation
15.4.3 Quadratic Interpolation
15.4.4 Improved Formulation
15.5 Efficient Remez Exchange Algorithm
15.6 Gradient Information
15.6.1 Property 1
15.6.2 Property 2
15.6.3 Property 3
15.6.4 Property 4
15.6.5 Property 5
15.7 Prescribed Specifications
15.8 Generalization
15.8.1 Antisymmetrical Impulse Response and Odd Filter Length
15.8.2 Even Filter Length
15.9 Digital Differentiators
15.9.1 Problem Formulation
15.9.2 First Derivative
15.9.3 Prescribed Specifications
15.10 Arbitrary Amplitude Responses
15.11 Multiband Filters
References
Additional References
Problems
Chapter 16. Design of Recursive Filters Using Optimization Methods
16.1 Introduction
16.2 Problem Formulation
16.3 Newton’s Method
16.4 Quasi-Newton Algorithms
16.4.1 Basic Quasi-Newton Algorithm
16.4.2 Updating Formulas for Matrix Sk+1
16.4.3 Inexact Line Searches
16.4.4 Practical Quasi-Newton Algorithm
16.5 Minimax Algorithms
16.6 Improved Minimax Algorithms
16.7 Design of Recursive Filters
16.7.1 Objective Function
16.7.2 Gradient Information
16.7.3 Stability
16.7.4 Minimum Filter Order
16.7.5 Use of Weighting
16.8 Design of Recursive Delay Equalizers
References
Additional References
Problems
Chapter 17. Wave Digital Filters
17.1 Introduction
17.2 Sensitivity Considerations
17.3 Wave Network Characterization
17.4 Element Realizations
17.4.1 Impedances
17.4.2 Voltage Sources
17.4.3 Series Wire Interconnection
17.4.4 Parallel Wire Interconnection
17.4.5 2-Port Adaptors
17.4.6 Transformers
17.4.7 Unit Elements
17.4.8 Circulators
17.4.9 Resonant Circuits
17.4.10 Realizability Constraint
17.5 Lattice Wave Digital Filters
17.5.1 Analysis
17.5.2 Alternative Lattice Configuration
17.5.3 Digital Realization
17.6 Ladder Wave Digital Filters
17.7 Filters Satisfying Prescribed Specifications
17.8 Frequency-Domain Analysis
17.9 Scaling
17.10 Elimination of Limit-Cycle Oscillations
17.11 Related Synthesis Methods
17.12 A Cascade Synthesis Based on the Wave Characterization
17.12.1 Generalized-Immittance Converters
17.12.2 Analog G-CGIC Configuration
17.12.3 Digital G-CGIC Configuration
17.12.4 Cascade Synthesis
17.12.5 Signal Scaling
17.12.6 Output Noise
17.13 Choice of Structure
References
Problems
Chapter 18. Digital Signal Processing Applications
18.1 Introduction
18.2 Sampling-Frequency Conversion
18.2.1 Decimators
18.2.2 Interpolators
18.2.3 Sampling Frequency Conversion by a Noninteger Factor
18.2.4 Design Considerations
18.3 Quadrature-Mirror-Image Filter Banks
18.3.1 Operation
18.3.2 Elimination of Aliasing Errors
18.3.3 Design Considerations
18.3.4 Perfect Reconstruction
18.4 Hilbert Transformers
18.4.1 Design of Hilbert Transformers
18.4.2 Single-Sideband Modulation
18.4.3 Sampling of Bandpassed Signals
18.5 Adaptive Digital Filters
18.5.1 Wiener Filters
18.5.2 Newton Algorithm
18.5.3 Steepest-Descent Algorithm
18.5.4 Least-Mean-Square Algorithm
18.5.5 Recursive Filters
18.5.6 Applications
18.6 Two-Dimensional Digital Filters
18.6.1 Two-Dimensional Convolution
18.6.2 Two-Dimensional z Transform
18.6.3 Two-Dimensional Transfer Function
18.6.4 Stability
18.6.5 Frequency-Domain Analysis
18.6.6 Types of 2-D Filters
18.6.7 Approximations
18.6.8 Applications
References
Additional References
Problems
Appendix A. Complex Analysis
A.1 Introduction
A.2 Complex Numbers
A.2.1 Complex Arithmetic
A.2.2 De Moivre’s Theorem
A.2.3 Euler’s Formula
A.2.4 Exponential Form
A.2.5 Vector Representation
A.2.6 Spherical Representation
A.3 Functions of a Complex Variable
A.3.1 Polynomials
A.3.2 Inverse Algebraic Functions
A.3.3 Trigonometric Functions and Their Inverses
A.3.4 Hyperbolic Functions and Their Inverses
A.3.5 Multi-Valued Functions
A.3.6 Periodic Function
A.3.7 Rational Algebraic Functions
A.4 Basic Principles of Complex Analysis
A.4.1 Limit
A.4.2 Differentiability
A.4.3 Analyticity
A.4.4 Zeros
A.4.5 Singularities
A.4.6 Zero-Pole Plots
A.5 Series
A.6 Laurent Theorem
A.7 Residue Theorem
A.8 Analytic Continuation
A.9 Conformal Transformations
References
Appendix B. Elliptic Functions
B.1 Introduction
B.2 Elliptic Integral of the First Kind
B.3 Elliptic Functions
B.4 Imaginary Argument
B.5 Formulas
B.6 Periodicity
B.7 Transformation
B.8 Series Representation
References
Index
Discrete Time Signal Processing by Alan V. Oppenheim , Ronald W. Schafer
Book Name:Discrete Time Signal Processing
Author: Alan V. Oppenheim , Ronald W. Schafer
Edition:ThirdPages: 1137
Click here to download
Content
Preface
The Companion Website
The Cover
Acknowledgments
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
2.9.6 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-2
8.8.3 Relationship between the DFT and the DCT-1
8.8.4 Relationship between the DFT and the DCT-2
8.8.5 Energy Compaction Property of the DCT-2
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 theWinograd 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
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