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Discrete-Time Signal Processing

ISBN: 9780137549207 | 0137549202
Edition: 3rd
Format: Hardcover
Publisher: Prentice Hall
Pub. Date: 1/1/2010

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SummaryTable of Contents
For senior/graduate-level courses in Discrete-Time Signal Processing. THE definitive, authoritative text on DSP - ideal for those with an introductory-level knowledge of signals and systems. Written by prominent, DSP pioneers, it provides thorough treatment of the fundamental theorems and properties of discrete-time linear systems, filtering, sampling, and discrete-time Fourier Analysis. By focusing on the general and universal concepts in discrete-time signal processing, it remains vital and relevant to the new challenges arising in the field -without limiting itself to specific technologies with relatively short life spans.
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List of Examples
xv
Prefacexix
Acknowledgementsxxv
Introduction
1(7)
DISCRETE-TIME SIGNALS AND SYSTEMS
8(86)
Introduction
8(1)
Discrete-Time Signals: Sequences
9(7)
Basic Sequences and Sequence Operations
11(5)
Discrete-Time Systems
16(6)
Memoryless Systems
18(1)
Linear Systems
18(2)
Time-Invariant Systems
20(1)
Causality
21(1)
Stability
21(1)
Linear Time-Invariant Systems
22(6)
Properties of Linear Time-Invariant Systems
28(6)
Linear Constant-Coefficient Difference Equations
34(6)
Frequency-Domain Representation of Discrete-Time Signals and Systems
40(8)
Eigenfunctions for Linear Time-Invariant Systems
40(6)
Suddenly Applied Complex Exponential Inputs
46(2)
Representation of Sequences by Fourier Transforms
48(7)
Symmetry Properties of the Fourier Transform
55(3)
Fourier Transform Theorems
58(7)
Linearity of the Fourier Transform
59(1)
Time Shifting and Frequency Shifting
59(1)
Time Reversal
60(1)
Differentiation in Frequency
60(1)
Parseval's Theorem
60(1)
The Convolution Theorem
60(1)
The Modulation or Windowing Theorem
61(4)
Discrete-Time Random Signals
65(5)
Summary
70(1)
Problems
70(24)
THE Z-TRANSFORM
94(46)
Introduction
94(1)
z-Transform
94(11)
Properties of the Region of Convergence for the z-Transform
105(6)
The Inverse z-Transform
111(8)
Inspection Method
111(1)
Partial Fraction Expansion
112(4)
Power Series Expansion
116(3)
z-Transform Properties
119(7)
Linearity
119(1)
Time Shifting
120(1)
Multiplication by an Exponential Sequence
121(1)
Differentiation of X (z)
122(1)
Conjugation of a Complex Sequence
123(1)
Time Reversal
123(1)
Convolution of Sequences
124(2)
Initial-Value Theorem
126(1)
Summary of Some z-Transform Properties
126(1)
Summary
126(1)
Problems
127(13)
SAMPLING OF CONTINUOUS-TIME SIGNALS
140(100)
Introduction
140(1)
Periodic Sampling
140(2)
Frequency-Domain Representation of Sampling
142(8)
Reconstruction of a Bandlimited Signal from Its Samples
150(3)
Discrete-Time Processing of Continuous-Time Signals
153(10)
Linear Time-Invariant Discrete-Time Systems
154(6)
Impulse Invariance
160(3)
Continuos-Time Processing of Discrete-Time Signals
163(4)
Changing the Sampling Rate Using Discrete-Time Processing
167(12)
Sampling Rate Reduction by an Integer Factor 167
167(5)
Increasing the Sampling Rate by an Integer Factor
172(4)
Changing the Sampling Rate by a Noninteger Factor
176(3)
Multirate Signal Processing
179(6)
Interchange of Filtering and Downsampling/Upsampling
179(1)
Polyphase Decompositions
180(2)
Polyphase Implementation of Decimation Filters
182(1)
Polyphase Implementation of Interpolation Filters
183(2)
Digital Processing of Analog Signals
185(16)
Prefiltering to Avoid Aliasing
185(2)
Analog-to-Digital (A/D) Conversion
187(6)
Analysis of Quantization Errors
193(4)
D/A Conversion
197(4)
Oversampling and Noise Shaping in A/D and D/A Conversion
201(12)
Oversampled A/D Conversion with Direct Quantization
201(5)
Oversampled A/D Conversion with Noise Shaping
206(4)
Oversampling and Noise Shaping in D/A Conversion
210(3)
Summary
213(1)
Problems
214(26)
TRANSFORM ANALYSIS OF LINEAR TIME-INVARIANT SYSTEMS
240(100)
Introduction
240(1)
The Frequency Response of LTI Systems
241(4)
Ideal Frequency-Selective Filters
241(1)
Phase Distortion and Delay
242(3)
System Functions for Systems Characterized by Linear Constant-Coefficient Difference Equations
245(8)
Stability and Causality
247(1)
Inverse Systems
248(2)
Impulse Response for Rational System Functions
250(3)
Frequency Response for Rational System Functions
253(17)
Frequency Response of a Single Zero or Pole
258(7)
Examples with Multiple Poles and Zeros
265(5)
Relationship between Magnitude and Phase
270(4)
All-Pass Systems
274(6)
Minimum-Phase Systems
280(11)
Minimum-Phase and All-Pass Decomposition
280(2)
Frequency-Response Compensation
282(5)
Properties of Minimum-Phase Systems
287(4)
Linear Systems with Generalized Linear Phase
291(20)
Systems with Linear Phase
292(3)
Generalized Linear Phase
295(2)
Causal Generalized Linear-Phase Systems
297(11)
Relation of FIR Linear-Phase Systems to Minimum-Phase Systems
308(3)
Summary
311(1)
Problems
312(28)
STRUCTURES FOR DISCRETE-TIME SYSTEMS
340(99)
Introduction
340(1)
Block Diagram Representation of Linear Constant-Coefficient Difference Equations
341(7)
Signal Flow Graph Representation of Linear Constant-Coefficient Difference Equations
348(6)
Basic Structures for IIR Systems
354(9)
Direct Forms
354(2)
Cascade Form
356(3)
Parallel Form
359(2)
Feedback in IIR Systems
361(2)
Transposed Forms
363(3)
Basic Network Structures for FIR systems
366(4)
Direct Form
367(1)
Cascade Form
367(1)
Structures for Linear-Phase FIR Systems
368(2)
Overview of Finite-Precision Numberical Effects
370(7)
Number Representations
371(3)
Quantization in Implementing Systems
374(3)
The Effects of Coefficient Quantization
377(14)
Effects of Coefficient quantization in FIR Systems
377(2)
Example of Coefficient Quantization in an Elliptic Filter
379(3)
Poles of Quantized Second-Order Sections
382(2)
Effects of Coefficient Quantization if FIR Systems
384(2)
Example of Quantization of an Optimum FIR Filter
386(4)
Maintaining Linear Phase
390(1)
Effects of Round-off Noise in Digital Filters
391(22)
Analysis of Direct-Form IIR Structures
391(8)
Scaling in Fixed-Point Implementations of IIR Systems
399(4)
Example of Analysis of a Cascade IIR Structure
403(7)
Analysis of Direct-Form FIR Systems
410(2)
Floating-Point Realizations of Discrete-Time Systems
412(1)
Zero-Input Limit Cycles in Fixed-Point Realizations of IIR Digital Filters
413(5)
Limit Cycles dueto Round-off and Truncation
414(2)
Limit Cycles Due to Overflow
416(1)
Avoiding Limit Cycles
417(1)
Summary
418(1)
Problems
419(20)
FILTER DESIGN TECHNIQUES
439(102)
Introduction
439(3)
Design of Discrete-Time IIR Filters from Continuous-Time Filters
442(23)
Filter Design by Impulse Invariance
443(7)
Bilinear Transformation
450(4)
Examples of Bilinear Transformation Design
454(11)
Design of FIR Filters by Windowing
465(13)
Properties of Commonly Used Windows
467(2)
Incorporation of Generalized Linear Phase
469(5)
The Kaiser Window Filter Design Method
474(4)
Relationship of the Kaiser Window to Other Windows
478(1)
Examples of FIR Filter Design by the Kaiser Window Method
478(8)
Highpass Filter
479(3)
Discrete-Time Differentiators
482(4)
Optimum Approximations of FIR Filters
486(17)
Optimal Type I Lowpass Filters
491(6)
Optimal Type II Lowpass Filters
497(1)
The Parks-McClellan Algorithm
498(3)
Characteristics of Optimum FIR Filters
501(2)
Examples of FIR Equiripple Approximation
503(7)
Lowpass Filter
503(3)
Compensation for Zero-Order Hold
506(1)
Bandpass Filter
507(3)
Comments on IIR and FIR Discrete-Time Filters
510(1)
Summary
511(1)
Problems
511(30)
The Discrete Fourier Transform
541(88)
Introduction
541(1)
Representation of Periodic Sequences: The Discrete Fourier Series
542(4)
Properties of the Discrete Fourier Series
546(5)
Linearity
546(1)
Shift of a Sequence
546(1)
Duality
547(1)
Symmetry Properties
547(1)
Periodic Convolution
548(2)
Summary of Properties of the DFS Representation of Perodic Sequences
550(1)
The Fourier Transform of Periodic Signals
551(4)
Sampling the Fourier Transform
555(4)
Fourier Representation of Finite-Duration Sequences: The Discrete Fourier Transform
559(5)
Properties of the Discrete Fourier Transform
564(12)
Linearity
564(1)
Circular Shift of a Sequence
564(3)
Duality
567(1)
Symmetry Properties
568(3)
Circular Convolution
571(4)
Summary of Properties of the Discrete Fourier Transform
575(1)
Linear Convolution Using the Discrete Fourier Transform
576(13)
Linear Convolution of Two Finite-Length Sequences
577(1)
Circular Convolution as Linear Convolution with Aliasing
577(5)
Implementing Linear Time-Invariant Systems Using the DFT
582(7)
The Discrete Consine Transform (DCT)
589(10)
Definitions of the DCT
589(1)
Definition of the DCT-1 and DCT-2
590(3)
Relationship between the DFT and the DCT-1
593(1)
Relationship between the DFT and the DCT-2
594(1)
Energy Compaction Property of the DCT-2
595(3)
Applications of the DCT
598(1)
Summary
599(30)
Problems
600(29)
COMPUTATION OF THE DISCRETE FOURIER TRANSFORM
629(64)
Introduction
629(1)
Efficient Computation of the Discrete Fourier Transform
630(3)
The Goertzel Algorithm
633(2)
Decimation-in-Time FFT Algorithms
635(11)
In-Place Computations
640(3)
Alternative Forms
643(3)
Decimation-inFrequency FFT Algiorithms
646(6)
In-Place Computation
650(1)
Alternative Forms
650(2)
Practical Considerations
652(3)
Indexing
652(2)
Coefficients
654(1)
Algorithms for More General Values of N
655(1)
Implementation of the DFT Using Convolution
655(6)
Overview of the Winograd Fourier Transform Algorithm
655(1)
The Chirp Transform Algorithm
656(5)
Effects of Finite Register Length
661(8)
Summary
669(1)
Problems
669(24)
Fourier Analysis of Signals Using the Discrete Fourier Transform
693(82)
Introduction
693(1)
Fourier Analysis of Signals Using the DFT
694(3)
DFT Analysis of Sinusoidal Signals
697(17)
The Effect of Windowing
698(5)
The Effect of Spectral Sampling
703(11)
The Time-Dependent Fourier Transform
714(8)
The Effect of the Window
717(1)
Sampling in Time and Frequency
718(4)
Block Convolution Using the Time-Dependent Fourier Transform
722(1)
Fourier Analysis of Nonstationary Signals
723(7)
Time-Dependent Fourier Analysis of Speech Signals
724(4)
Time-Dependent Fourier Analysis of Radar Signals
728(2)
Fourier Analysis of Stationary Random Signals: The Periodogram
730(13)
The Periodogram
731(2)
Properties of the Periodogram
733(4)
Periodogram Averaging
737(2)
Computation of Average Periodograms Using the DFT
739(1)
An Example of Periodogram Analysis
739(4)
Spectrum Analysis of Random Signals Using Estimates of the Autocorrelation Sequence
743(11)
Computing Correlation and Power Spectrum Estimates Using the DFT
746(2)
An Example of Power Spectrum Estimation Based on Estimation of the Autocorrelation Sequence
748(6)
Summary
754(1)
Problems
755(20)
Discrete Hilbert Transforms
775(36)
Introduction
775(2)
Real- and Imaginary-Part Sufficiency of the Fourier Transform for Causal Sequences
777(5)
Sufficiency Theorems for Finite-Length Sequences
782(6)
Relationships Between Magnitude and Phase
788(1)
Hilbert Transform Relations for Complex Sequences
789(12)
Design of Hilbert Transformers
792(4)
Representation of Bandpass Signals
796(3)
Bandpass Sampling
799(2)
Summary
801(1)
Problems
802(9)
Appendix A Random Signals811(1)
Discrete-Time Random Processes811(2)
Averages813(1)
Definitions813(2)
Time Averages815(2)
Properties of Correlation and Covariance Sequences817(1)
Fourier Transform Representation of Random Signals818(2)
Use of the z-Transform in Average Power Computations820(4)
Appendix B Continuous-Time Filters824(1)
Butterworth Lowpass Filters824(2)
Chebyshev Filters826(2)
Elliptic Filters828(2)
Appendix C Answers to Selected Basic Problems830(21)
Bibliography851(8)
Index859

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