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《数字信号处理精华》(Essentials of Digital Signal Processing)文字版[PDF]

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    出版社Cambridge University Press
    发行时间2014年
    语言英文
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中文名数字信号处理精华
原名Essentials of Digital Signal Processing
别名
译者
图书分类科技
资源格式PDF
版本文字版
出版社Cambridge University Press
书号9781107059320
发行时间2014年
地区美国
语言英文
简介

IPB Image
内容简介:
This textbook o ers a fresh approach to digital signal processing (DSP) that combines heuristic reasoning and physical appreciation with sound mathematical methods to illuminate DSP concepts and practices. It uses metaphors, analogies, and creative explanations along with carefully selected examples and exercises to provide deep and intuitive insights into DSP concepts.
Practical DSP requires hybrid systems including both discrete- and continuous-time components. This book follows a holistic approach and presents discrete-time processing as a seamless continuation of continuous-time signals and systems, beginning with a review of continuous-time signals and systems, frequency response, and ltering. The synergistic combination of continuous-time and discrete-time perspectives leads to a deeper appreciation and understanding of DSP concepts and practices.
Notable Features
1. Written for upper-level undergraduates
2. Provides an intuitive understanding and physical appreciation of essential DSP concepts without sacri cing mathematical rigor
3. Illustrates concepts with 500 high-quality gures, more than 170 fully worked examples, and hundreds of end-of-chapter problems
4. Encourages student learning with more than 150 drill exercises, including complete and detailed solutions
5. Maintains strong ties to continuous-time signals and systems concepts, with immediate access to background material with a notationally consistent format, helping readers build on their previous knowledge
6. Seamlessly integrates MATLAB throughout the text to enhance learning
7. Develops MATLAB code from a basic level to reinforce connections to underlying theory and sound DSP practice

内容截图:
IPB Image
作者介绍:
B. P. Lathi holds a PhD in Electrical Engineering from Stanford University and was previously a Professor of Electrical Engineering at California State University, Sacramento. He is the author of eight books, including Signal Processing and Linear Systems (second ed., 2004) and, with Zhi Ding, Modern Digital and Analog Communications Systems (fourth ed., 2009).

Roger Green is an Associate Professor of Electrical and Computer Engineering at North Dakota State University. He holds a PhD from the University of Wyoming. He is co-author, with B. P. Lathi, on the second edition of Signal Processing and Linear Systems.
备注说明:
应网友要求,更新Lathi B.P较新发行著作。



目录

Preface..........................................................................................vii
1 Review of Continuous-Time Signals and Systems ....................................1
1.1 Signals and Signal Categorizations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.1.1 Continuous-Time and Discrete-Time Signals . . . . . . . . . . . . . . . . . . . 3
1.1.2 Analog and Digital Signals . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.2 Operations on the Independent CT Variable . . . . . . . . . . . . . . . . . . . . . . . 4
1.2.1 CT Time Shifting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.2.2 CT Time Scaling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.2.3 CT Time Reversal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.2.4 Combined CT Time Shifting and Scaling . . . . . . . . . . . . . . . . . . . . 6
1.3 CT SignalModels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.3.1 CT Unit Step Function u(t) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.3.2 CT Unit Gate Function Π(t) . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.3.3 CT Unit Triangle Function Λ(t) . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.3.4 CT Unit Impulse Function δ(t) . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.3.5 CT Exponential Function est . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
1.3.6 CT Interpolation Function sinc(t) . . . . . . . . . . . . . . . . . . . . . . . . 13
1.4 CT Signal Classifications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
1.4.1 Causal, Noncausal, and Anti-Causal CT Signals . . . . . . . . . . . . . . . . . 15
1.4.2 Real and Imaginary CT Signals . . . . . . . . . . . . . . . . . . . . . . . . . . 16
1.4.3 Even and Odd CT Signals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
1.4.4 Periodic and Aperiodic CT Signals . . . . . . . . . . . . . . . . . . . . . . . . 21
1.4.5 CT Energy and Power Signals . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
1.4.6 Deterministic and Probabilistic Signals . . . . . . . . . . . . . . . . . . . . . . 25
1.5 CT Systems and Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
1.5.1 Linearity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
1.5.2 Time Invariance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
1.5.3 The Zero-State Response of an LTIC System . . . . . . . . . . . . . . . . . . 28
1.5.4 Causality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
1.5.5 Stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
1.6 Foundations of Frequency-Domain Analysis . . . . . . . . . . . . . . . . . . . . . . . 30
1.6.1 LTIC System Response to an Everlasting Exponential est . . . . . . . . . . . 30
1.7 The Fourier Series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
1.7.1 Exponential Formof the Fourier Series . . . . . . . . . . . . . . . . . . . . . . 34
1.7.2 Trigonometric and Compact Trigonometric Forms . . . . . . . . . . . . . . . 37
1.7.3 Convergence of a Series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
1.8 The Fourier Transform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
1.9 Fourier TransformProperties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
1.9.1 Duality Property . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
1.9.2 Linearity Property . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
1.9.3 Complex-Conjugation Property . . . . . . . . . . . . . . . . . . . . . . . . . . 52
1.9.4 Scaling Property . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
1.9.5 Time-Shifting Property . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
1.9.6 Time-Differentiation and Time-Integration Properties . . . . . . . . . . . . . 59
1.9.7 Time-Domain Convolution Property . . . . . . . . . . . . . . . . . . . . . . . 59
1.9.8 Correlation and the Correlation Property . . . . . . . . . . . . . . . . . . . . 61
1.9.9 Extending Fourier Transform Properties to the Fourier Series . . . . . . . . . 66
1.10 The Laplace Transform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
1.10.1 Connection between the Fourier and Laplace Transforms . . . . . . . . . . . . 70
1.10.2 Laplace TransformProperties . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
1.11 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
2 Continuous-Time Analog Filters 85
2.1 Frequency Response of an LTIC System . . . . . . . . . . . . . . . . . . . . . . . . . 85
2.1.1 Pole-Zero Plots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
2.2 Signal Transmission through LTIC Systems . . . . . . . . . . . . . . . . . . . . . . . 92
2.2.1 Distortionless Transmission . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
2.2.2 Real Bandpass Systems and Group Delay . . . . . . . . . . . . . . . . . . . . 97
2.3 Ideal and Realizable Filters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
2.4 Data Truncation byWindows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
2.4.1 Impairments Caused byWindowing . . . . . . . . . . . . . . . . . . . . . . . 104
2.4.2 Lowpass Filter Design UsingWindows . . . . . . . . . . . . . . . . . . . . . . 106
2.4.3 Remedies for Truncation Impairments . . . . . . . . . . . . . . . . . . . . . . 109
2.4.4 CommonWindow Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
2.5 Specification of Practical Filters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
2.6 Analog Filter Transformations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
2.6.1 Lowpass-to-LowpassTransformation . . . . . . . . . . . . . . . . . . . . . . . 115
2.6.2 Lowpass-to-HighpassTransformation . . . . . . . . . . . . . . . . . . . . . . . 116
2.6.3 Lowpass-to-Bandpass Transformation . . . . . . . . . . . . . . . . . . . . . . 117
2.6.4 Lowpass-to-BandstopTransformation . . . . . . . . . . . . . . . . . . . . . . 118
2.7 Practical Filter Families . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
2.7.1 Butterworth Filters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
2.7.2 Chebyshev Filters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
2.7.3 Inverse Chebyshev Filters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
2.7.4 Elliptic Filters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144
2.7.5 Bessel-Thomson Filters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
2.8 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149
3 Sampling: The Bridge from Continuous to Discrete 155
3.1 Sampling and the Sampling Theorem. . . . . . . . . . . . . . . . . . . . . . . . . . . 155
3.1.1 Practical Sampling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161
3.2 Signal Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164
3.3 PracticalDifficulties in Sampling and Reconstruction . . . . . . . . . . . . . . . . . . 168
3.3.1 Aliasing in Sinusoids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173
3.4 Sampling of Bandpass Signals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176
3.5 Time-Sampling Dual: The Spectral Sampling Theorem . . . . . . . . . . . . . . . . . 181
3.6 Analog-to-Digital Conversion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185
3.6.1 Analog-to-Digital Converter Transfer Characteristics . . . . . . . . . . . . . . 189
3.6.2 Analog-to-Digital Converter Errors . . . . . . . . . . . . . . . . . . . . . . . . 194
3.6.3 Analog-to-Digital Converter Implementations . . . . . . . . . . . . . . . . . . 196
3.7 Digital-to-Analog Conversion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199
3.7.1 Sources of Distortion in Signal Reconstruction . . . . . . . . . . . . . . . . . 200
3.8 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202
4 Discrete-Time Signals and Systems 212
4.1 Operations on the Independent DT Variable . . . . . . . . . . . . . . . . . . . . . . . 214
4.1.1 DT Time Shifting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214
4.1.2 DT Time Reversal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215
4.1.3 DT Time Scaling: Sampling Rate Conversion . . . . . . . . . . . . . . . . . . 216
4.2 DT SignalModels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219
4.2.1 DT Unit Step Function u[n] . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219
4.2.2 DT Unit Impulse Function δ[n] . . . . . . . . . . . . . . . . . . . . . . . . . . 220
4.2.3 DT Exponential Function zn . . . . . . . . . . . . . . . . . . . . . . . . . . . 222
4.3 DT Signal Classifications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 231
4.3.1 Causal, Noncausal, and Anti-Causal DT Signals . . . . . . . . . . . . . . . . 231
4.3.2 Real and ImaginaryDT Signals . . . . . . . . . . . . . . . . . . . . . . . . . . 232
4.3.3 Even and Odd DT Signals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232
4.3.4 Periodic and Aperiodic DT Signals . . . . . . . . . . . . . . . . . . . . . . . . 233
4.3.5 DT Energy and Power Signals . . . . . . . . . . . . . . . . . . . . . . . . . . 236
4.4 DT Systems and Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 238
4.4.1 The Order and General Form of Difference Equations . . . . . . . . . . . . . 245
4.4.2 Kinship of Difference Equations to Differential Equations . . . . . . . . . . . 246
4.4.3 Advantages of Digital Signal Processing . . . . . . . . . . . . . . . . . . . . . 248
4.5 DT SystemProperties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 248
4.5.1 Time Invariance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 248
4.5.2 Linearity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 250
4.5.3 The Zero-State Response of an LTID System . . . . . . . . . . . . . . . . . . 252
4.5.4 Causality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 254
4.5.5 Stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 256
4.5.6 Memory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 256
4.5.7 Invertibility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 257
4.6 Digital Resampling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 257
4.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 261
5 Time-Domain Analysis of Discrete-Time Systems 270
5.1 Iterative Solutions to Difference Equations . . . . . . . . . . . . . . . . . . . . . . . . 270
5.2 Operator Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 275
5.3 The Zero-Input Response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 277
5.3.1 Insights into the Zero-Input Behavior of a System . . . . . . . . . . . . . . . 282
5.4 The Unit Impulse Response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 284
5.4.1 Closed-FormSolution of the Impulse Response . . . . . . . . . . . . . . . . . 285
5.5 The Zero-State Response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 288
5.5.1 Convolution Sum Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . 291
5.5.2 Graphical Procedure for the Convolution Sum . . . . . . . . . . . . . . . . . 294
5.5.3 Interconnected Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 300
5.5.4 LTID System Response to an Everlasting Exponential zn . . . . . . . . . . . 303
5.6 Total Response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 304
5.7 System Stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 305
5.7.1 External (BIBO) Stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 306
5.7.2 Internal (Asymptotic) Stability . . . . . . . . . . . . . . . . . . . . . . . . . . 306
5.8 Intuitive Insights into System Behavior . . . . . . . . . . . . . . . . . . . . . . . . . . 311
5.8.1 Dependence of System Behavior on CharacteristicModes . . . . . . . . . . . 311
5.8.2 Response Time of a System: The System Time Constant . . . . . . . . . . . 312
5.8.3 Time Constant and Rise Time of a System . . . . . . . . . . . . . . . . . . . 314
5.8.4 Time Constant and Filtering . . . . . . . . . . . . . . . . . . . . . . . . . . . 314
5.8.5 Time Constant and Pulse Dispersion . . . . . . . . . . . . . . . . . . . . . . . 315
5.8.6 The Resonance Phenomenon . . . . . . . . . . . . . . . . . . . . . . . . . . . 315
5.9 Classical Solution of Linear Difference Equations . . . . . . . . . . . . . . . . . . . . 317
5.10 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 322
6 Discrete-Time Fourier Analysis 331
6.1 The Discrete-Time Fourier Transform . . . . . . . . . . . . . . . . . . . . . . . . . . 331
6.1.1 The Nature of Fourier Spectra . . . . . . . . . . . . . . . . . . . . . . . . . . 337
6.1.2 Obtaining the DTFT from the CTFT . . . . . . . . . . . . . . . . . . . . . . 338
6.1.3 DTFT Tables and the Nuisance of Periodicity . . . . . . . . . . . . . . . . . . 340
6.2 Properties of the DTFT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 343
6.2.1 Duality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 343
6.2.2 Linearity Property . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 343
6.2.3 Complex-Conjugation Property . . . . . . . . . . . . . . . . . . . . . . . . . . 343
6.2.4 Time Scaling and the Time-Reversal Property . . . . . . . . . . . . . . . . . 344
6.2.5 Time-Shifting Property . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 345
6.2.6 Frequency-Differentiation Property . . . . . . . . . . . . . . . . . . . . . . . . 350
6.2.7 Time-Domain and Frequency-Domain Convolution Properties . . . . . . . . . 351
6.2.8 Correlation and the Correlation Property . . . . . . . . . . . . . . . . . . . . 354
6.3 LTID System Analysis by the DTFT . . . . . . . . . . . . . . . . . . . . . . . . . . . 355
6.3.1 Distortionless Transmission . . . . . . . . . . . . . . . . . . . . . . . . . . . . 359
6.3.2 Ideal and Realizable Filters . . . . . . . . . . . . . . . . . . . . . . . . . . . . 362
6.4 Connection between the DTFT and the CTFT . . . . . . . . . . . . . . . . . . . . . 364
6.5 Digital Processing of Analog Signals . . . . . . . . . . . . . . . . . . . . . . . . . . . 370
6.5.1 AMathematical Representation. . . . . . . . . . . . . . . . . . . . . . . . . . 371
6.5.2 Time-Domain Criterion: The Impulse Invariance Method . . . . . . . . . . . 373
6.6 Digital Resampling: A Frequency-Domain Perspective . . . . . . . . . . . . . . . . . 379
6.6.1 Using Bandlimited Interpolation to Understand Resampling . . . . . . . . . . 380
6.6.2 Downsampling and Decimation . . . . . . . . . . . . . . . . . . . . . . . . . . 383
6.6.3 Interpolation and Upsampling . . . . . . . . . . . . . . . . . . . . . . . . . . . 387
6.6.4 Time-Domain Characterizations . . . . . . . . . . . . . . . . . . . . . . . . . 391
6.6.5 Fractional Sampling Rate Conversion . . . . . . . . . . . . . . . . . . . . . . 394
6.7 Generalization of the DTFT to the z-Transform. . . . . . . . . . . . . . . . . . . . . 395
6.8 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 397
7 Discrete-Time System Analysis Using the z-Transform 410
7.1 The z-Transform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 410
7.1.1 The Bilateral z-Transform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 410
7.1.2 The Unilateral z-Transform . . . . . . . . . . . . . . . . . . . . . . . . . . . . 416
7.2 The Inverse z-Transform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 419
7.2.1 Inverse z-Transformby Power Series Expansion . . . . . . . . . . . . . . . . . 425
7.3 Properties of the z-Transform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 427
7.3.1 Linearity Property . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 427
7.3.2 Complex-Conjugation Property . . . . . . . . . . . . . . . . . . . . . . . . . . 427
7.3.3 Time Scaling and the Time-Reversal Property . . . . . . . . . . . . . . . . . 428
7.3.4 Time-Shifting Property . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 428
7.3.5 z-Domain Scaling Property . . . . . . . . . . . . . . . . . . . . . . . . . . . . 432
7.3.6 z-Domain Differentiation Property . . . . . . . . . . . . . . . . . . . . . . . . 433
7.3.7 Time-Domain Convolution Property . . . . . . . . . . . . . . . . . . . . . . . 433
7.3.8 Initial and Final Value Theorems . . . . . . . . . . . . . . . . . . . . . . . . . 435
7.4 z-TransformSolution of Linear Difference Equations . . . . . . . . . . . . . . . . . . 436
7.4.1 Zero-State Response of LTID Systems: The Transfer Function . . . . . . . . 439
7.5 Block Diagrams and System Realization . . . . . . . . . . . . . . . . . . . . . . . . . 445
7.5.1 Direct FormRealizations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 447
7.5.2 Transposed Realizations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 451
7.5.3 Cascade and ParallelRealizations . . . . . . . . . . . . . . . . . . . . . . . . 453
7.6 Frequency Response of Discrete-Time Systems . . . . . . . . . . . . . . . . . . . . . 457
7.6.1 Frequency-Response from Pole-Zero Locations . . . . . . . . . . . . . . . . . 462
7.7 FiniteWord-Length Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 469
7.7.1 FiniteWord-Length Effects on Poles and Zeros . . . . . . . . . . . . . . . . . 469
7.7.2 FiniteWord-Length Effects on Frequency Response . . . . . . . . . . . . . . 472
7.8 Connection between the Laplace and z-Transforms . . . . . . . . . . . . . . . . . . . 474
7.9 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 476
8 Digital Filters 485
8.1 Infinite Impulse Response Filters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 485
8.1.1 The Impulse InvarianceMethod Revisited . . . . . . . . . . . . . . . . . . . . 486
8.1.2 The Bilinear Transform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 491
8.1.3 The Bilinear Transform with Prewarping . . . . . . . . . . . . . . . . . . . . 497
8.1.4 Highpass, Bandpass, and Bandstop Filters . . . . . . . . . . . . . . . . . . . . 501
8.1.5 Realization of IIR Filters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 508
8.2 Finite Impulse Response Filters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 511
8.2.1 Linear Phase FIR Filters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 511
8.2.2 Realization of FIR Filters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 515
8.2.3 Windowing in FIR Filters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 517
8.2.4 Time-DomainMethods of FIR Filter Design . . . . . . . . . . . . . . . . . . . 521
8.2.5 Window Method FIR Filter Design for Given Specifications . . . . . . . . . . 529
8.2.6 Frequency-DomainMethods of FIR Filter Design . . . . . . . . . . . . . . . . 537
8.2.7 Frequency-Weighted Least-Squares FIR Filter Design . . . . . . . . . . . . . 544
8.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 552
9 Discrete Fourier Transform 559
9.1 The Discrete Fourier Transform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 560
9.1.1 The Picket Fence Effect and Zero Padding . . . . . . . . . . . . . . . . . . . . 563
9.1.2 Matrix Representation of the DFT and Its Inverse . . . . . . . . . . . . . . . 565
9.1.3 DFT Interpolation to Obtain the DTFT . . . . . . . . . . . . . . . . . . . . . 567
9.2 Uniqueness: Why Confine x[n] to 0 ≤ n ≤ N −1? . . . . . . . . . . . . . . . . . . . . 569
9.2.1 Modulo-N Operation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 572
9.2.2 Circular Representation of an N-Length Sequence . . . . . . . . . . . . . . . 573
9.3 Properties of the DFT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 579
9.3.1 Duality Property . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 579
9.3.2 Linearity Property . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 579
9.3.3 Complex-Conjugation Property . . . . . . . . . . . . . . . . . . . . . . . . . . 580
9.3.4 Time-Reversal Property . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 580
9.3.5 Circular Shifting Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . 580
9.3.6 Circular Convolution Properties . . . . . . . . . . . . . . . . . . . . . . . . . 581
9.3.7 Circular Correlation Property . . . . . . . . . . . . . . . . . . . . . . . . . . . 582
9.4 Graphical Interpretation of Circular Convolution . . . . . . . . . . . . . . . . . . . . 583
9.4.1 Circular and Linear Convolution . . . . . . . . . . . . . . . . . . . . . . . . . 585
9.4.2 Aliasing in Circular Convolution . . . . . . . . . . . . . . . . . . . . . . . . . 588
9.5 Discrete-Time Filtering Using the DFT . . . . . . . . . . . . . . . . . . . . . . . . . 590
9.5.1 Block Convolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 593
9.6 Goertzel’s Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 600
9.7 The Fast Fourier Transform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 603
9.7.1 Decimation-in-Time Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . 604
9.7.2 Decimation-in-Frequency Algorithm . . . . . . . . . . . . . . . . . . . . . . . 609
9.8 The Discrete-Time Fourier Series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 612
9.9 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 617
A------MATLAB ..................................................................................625
B------Useful Tables .............................................................................640
C------Drill Solutions ..............................................................................646
Index..................................................................................................731

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