数字信号处理 系统分析与设计 原书第2版 英文版2025|PDF|Epub|mobi|kindle电子书版本百度云盘下载

数字信号处理 系统分析与设计 原书第2版 英文版PDF格式电子书版下载

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Introduction1

1 Discrete-time signals and systems5

1.1 Introduction5

1.2 Discrete-time signals6

1.3 Discrete-time systems10

1.3.1 Linearity10

1.3.2 Time invariance11

1.3.3 Causality11

1.3.4 Impulse response and convolution sums14

1.3.5 Stability16

1.4 Difference equations and time-domain response17

1.4.1 Recursive×nonrecursive systems21

1.5 Solving difference equations22

1.5.1 Computing impulse responses31

1.6 Sampling of continuous-time signals33

1.6.1 Basic principles34

1.6.2 Sampling theorem34

1.7 Random signals53

1.7.1 Random variable54

1.7.2 Random processes58

1.7.3 Filtering a random signal60

1.8 Do-it-yourself:discrete-time signals and systems62

1.9 Discrete-time signals and systems with MATLAB67

1.10 Summary68

1.11 Exercises68

2 The z and Fourier transforms75

2.1 Introduction75

2.2 Definition of the z transform76

2.3 Inverse z transform83

2.3.1 Computation based on residue theorem84

2.3.2 Computation based on partial-fraction expansions87

2.3.4 Computation based on series expansion92

2.4 Properties of the z transform94

2.4.1 Linearity94

2.4.2 Time reversal94

2.4.3 Time-shift theorem95

2.4.4 Multiplication by an exponential95

2.4.5 Complex differentiation95

2.4.6 Complex conjugation96

2.4.7 Real and imaginary sequences97

2.4.8 Initial-value theorem97

2.4.9 Convolution theorem98

2.4.10 Product of two sequences98

2.4.11 Parseval's theorem100

2.4.12 Table of basic z transforms101

2.5 Transfer functions104

2.6 Stability in the z domain106

2.7 Frequency response109

2.8 Fourier transform115

2.9 Properties of the Fourier transform120

2.9.1 Linearity120

2.9.2 Time reversal120

2.9.3 Time-shift theorem120

2.9.4 Multiplication by a complex exponential(frequency shift,modulation)120

2.9.5 Complex differentiation120

2.9.6 Complex conjugation121

2.9.7 Real and imaginary sequences121

2.9.8 Symmetric and antisymmetric sequences122

2.9.9 Convolution theorem123

2.9.10 Product of two sequences123

2.9.11 Parseval's theorem123

2.10 Fourier transform for periodic sequences123

2.11 Random signals in the transform domain125

2.11.1 Power spectral density125

2.11.2 Whitenoise128

2.12 Do-it-yourself:the z and Fourier transforms129

2.13 The z and Fourier transforms with MATLAB135

2.14 Summary137

2.15 Exercises137

3 Discrete transforms143

3.1 Introduction143

3.2 Discrete Fourier transform144

3.3 Properties of the DFT153

3.3.1 Linearity153

3.3.2 Time reversal153

3.3.3 Time-shift theorem153

3.3.4 Circular frequency-shift theorem(modulation theorem)156

3.3.5 Circular convolution in time157

3.3.6 Correlation158

3.3.7 Complex conjugation159

3.3.8 Real and imaginary sequences159

3.3.9 Symmetric and antisymmetric sequences160

3.3.10 Parseval's theorem162

3.3.11 Relationship between the DFT and the z transform163

3.4 Digital filtering using the DFT164

3.4.1 Linear and circular convolutions164

3.4.2 Overlap-and-add method168

3.4.3 Overlap-and-save method171

3.5 Fast Fourier transform175

3.5.1 Radix-2 algorithm with decimation in time176

3.5.2 Decimation in frequency184

3.5.3 Radix-4 algorithm187

3.5.4 Algorithms for arbitrary values of N192

3.5.5 Alternative techniques for determining the DFT193

3.6 Other discrete transforms194

3.6.1 Discrete transforms and Parseval's theorem195

3.6.2 Discrete transforms and orthogonality196

3.6.3 Discrete cosine transform199

3.6.4 A family of sine and cosine transforms203

3.6.5 Discrete Hartley transform205

3.6.6 Hadamard transform206

3.6.7 Other important transforms207

3.7 Signal representations208

3.7.1 Laplace transform208

3.7.2 The z transform208

3.7.3 Fourier transform(continuous time)209

3.7.4 Fourier transform(discrete time)209

3.7.5 Fourier series210

3.7.6 Discrete Fourier transform210

3.8 Do-it-yourself:discrete transforms211

3.9 Discrete transforms with MATLAB215

3.10 Summary216

3.11 Exercises217

4 Digital filters222

4.1 Introduction222

4.2 Basic structures of nonrecursive digital filters222

4.2.1 Direct form223

4.2.2 Cascade form224

4.2.3 Linear-phase forms225

4.3 Basic structures of recursive digital filters232

4.3.1 Direct forms232

4.3.2 Cascade form236

4.3.3 Parallel form237

4.4 Digital network analysis241

4.5 State-space description244

4.6 Basic properties of digital networks246

4.6.1 Tellegen's theorem246

4.6.2 Reciprocity248

4.6.3 Interreciprocity249

4.6.4 Transposition249

4.6.5 Sensitivity250

4.7 Useful building blocks257

4.7.1 Second-order building blocks257

4.7.2 Digital oscillators260

4.7.3 Comb filter261

4.8 Do-it-yourself:digital filters263

4.9 Digital filter forms with MATLAB266

4.10 Summary270

4.11 Exercises270

5 FIR filter approximations277

5.1 Introduction277

5.2 Ideal characteristics of standard filters277

5.2.1 Lowpass,highpass,bandpass,and bandstop filters278

5.2.2 Differentiators280

5.2.3 Hilbert transformers281

5.2.4 Summary283

5.3 FIR filter approximation by frequency sampling283

5.4 FIR filter approximation with window functions291

5.4.1 Rectangular window294

5.4.2 Triangular windows295

5.4.3 Hamming and Hann windows296

5.4.4 Blackman window297

5.4.5 Kaiser window299

5.4.6 Dolph-Chebyshev window306

5.5 Maximally flat FIR filter approximation309

5.6 FIR filter approximation by optimization313

5.6.1 Weighted least-squares method317

5.6.2 Chebyshev method321

5.6.3 WLS-Chebyshev method327

5.7 Do-it-yourself:FIR filter approximations333

5.8 FIR filter approximation with MATLAB336

5.9 Summary342

5.10 Exercises343

6 IIR filter approximations349

6.1 Introduction349

6.2 Analog filter approximations350

6.2.1 Analog filter specification350

6.2.2 Butterworth approximation351

6.2.3 Chebyshev approximation353

6.2.4 Elliptic approximation356

6.2.5 Frequency transformations359

6.3 Continuous-time to discrete-time transformations368

6.3.1 Impulse-invafiance method368

6.3.2 Bilinear transformation method372

6.4 Frequency transformation in the discrete-time domain378

6.4.1 Lowpass-to-lowpass ffansformation379

6.4.2 Lowpass-to-highpass transformation380

6.4.3 Lowpass-to-bandpass transformation380

6.4.4 Lowpass-to-bandstop transformation381

6.4.5 Variable-cutoff filter design381

6.5 Magnitude and phase approximation382

6.5.1 Basic principles382

6.5.2 Multivariable function minimization method387

6.5.3 Alternative methods389

6.6 Time-domain approximation391

6.6.1 Approximate approach393

6.7 Do-it-yourself:IIR filter approximations394

6.8 IIR filter approximation with MATLAB399

6.9 Summary403

6.10 Exercises404

7 Spectral estimation409

7.1 Introduction409

7.2 Estimation theory410

7.3 Nonparametric spectral estimation411

7.3.1 Periodogram411

7.3.2 Periodogrum variations413

7.3.3 Minimum-variance spectral estimator416

7.4 Modeling theory419

7.4.1 Rational transfer-function models419

7.4.2 Yule-Walker equations423

7.5 Parametric spectral estimation426

7.5.1 Linear prediction426

7.5.2 Covariance method430

7.5.3 Autocorrelation method431

7.5.4 Levinson-Durbin algorithm432

7.5.5 Burg's method434

7.5.6 Relationship of the Levinson-Durbin algorithm to a lattice structure438

7.6 Wiener filter438

7.7 Other methods for spectral estimation441

7.8 Do-it-yourself:spectral estimation442

7.9 Spectral estimation with MATLAB449

7.10 Summary450

7.11 Exercises451

8 Multirate systems455

8.1 Introduction455

8.2 Basic principles455

8.3 Decimation456

8.4 Interpolation462

8.4.1 Examples of interpolators464

8.5 Rational sampling-rate changes465

8.6 Inverse operations466

8.7 Noble identities467

8.8 Polyphase decompositions469

8.9 Commutator models471

8.10 Decimation and interpolation for efficient filter implementation474

8.10.1 Narrowband FIR filters474

8.10.2 Wideband FIR filters with narrow transition bands477

8.11 Overlapped block filtering479

8.11.1 Nonoverlapped case480

8.11.2 Overlapped input and output483

8.11.3 Fast convolution structure Ⅰ487

8.11.4 Fast convolution structure Ⅱ487

8.12 Random signals in multirate systems490

8.12.1 Interpolated random signals491

8.12.2 Decimated random signals492

8.13 Do-it-yourself:multirate systems493

8.14 Multirate systems with MATLAB495

8.15 Summary497

8.16 Exercises498

9 Filter banks503

9.1 Introduction503

9.2 Filter banks503

9.2.1 Decimation of a bandpass signal504

9.2.2 Inverse decimation of a bandpass signal505

9.2.3 Critically decimated M-band filter banks506

9.3 Perfect reconstruction507

9.3.1 M-band filter banks in terms of polyphase components507

9.3.2 Perfect reconstruction M-band filter banks509

9.4 Analysis of M-band filter banks517

9.4.1 Modulation matrix representation518

9.4.2 Time-domain analysis520

9.4.3 Orthogonality and biorthogonality in filter banks529

9.4.4 Transmultiplexers534

9.5 General two-band perfect reconstruction filter banks535

9.6 QMF filterbanks540

9.7 CQF filterbanks543

9.8 Block transforns548

9.9 Cosine-modulated filter banks554

9.9.1 The optimization problem in the design of cosine-modulated filter banks559

9.10 Lapped transforms563

9.10.1 Fast algorithms and biorthogonal LOT573

9.10.2 Generalized LOT576

9.11 Do-it-yourself:filter banks581

9.12 Filter banks with MATLAB594

9.13 Summary594

9.14 Exercises595

10 Wavelet transforms599

10.1 Introduction599

10.2 Wavelet transforms599

10.2.1 Hierarchical filter banks599

10.2.2 Wavelets601

10.2.3 Scaling functions605

10.3 Relation between x(t)and x(n)606

10.4 Wavelet transforms and time-frequency analysis607

10.4.1 The short-time Fourier transform607

10.4.2 The continuous-time wavelet transform612

10.4.3 Sampling the continuous-time wavelet transform:the discrete wavelet transform614

10.5 Multiresolution representation617

10.5.1 Biorthogonal multiresolution representation620

10.6 Wavelet transforms and filter banks623

10.6.1 Relations between the filter coefficients629

10.7 Regularity633

10.7.1 Additional constraints imposed on the filter banks due to the regularity condition634

10.7.2 Apractical estimate of regularity635

10.7.3 Number of vanishing moments636

10.8 Examples of wavelets638

10.9 Wavelet transforms of images641

10.10 Wavelet transforms of finite-length signals646

10.10.1 Periodic signal extension646

10.10.2 Symmetric signal extensions648

10.11 Do-it-yourself:wavelet transforms653

10.12 Wavelets with MATLAB659

10.13 Summary664

10.14 Exercises665

11 Finite-precision digital signal processing668

11.1 Introduction668

11.2 Binary number representation670

11.2.1 Fixed-point representations670

11.2.2 Signed power-of-two representation672

11.2.3 Floating-point representation673

11.3 Basic elements674

11.3.1 Properties of the two's-complement representation674

11.3.2 Serial adder674

11.3.3 Serial multiplier676

11.3.4 Parallel adder684

11.3.5 Parallel multiplier684

11.4 Distributed arithmetic implementation685

11.5 Product quantization691

11.6 Signal scaling697

11.7 Coefficient quantization706

11.7.1 Deterministic sensitivity criterion708

11.7.2 Statistical forecast of the wordlength711

11.8 Limit cycles715

11.8.1 Granular limit cycles715

11.8.2 Overflow limit cycles717

11.8.3 Elimination of zero-input limit cycles719

11.8.4 Elimination of constant-input limit cycles725

11.8.5 Forced-response stability ofdigital filters with nonlinearities due to overflow729

11.9 Do-it-yourself:finite-precision digital signal processing732

11.10 Finite-precision digital signal processing with MATLAB735

11.11 Summary735

11.12 Exercises736

12 Efficient FIR structures740

12.1 Introduction740

12.2 Latticeform740

12.2.1 Filter banks using the lattice form742

12.3 Polyphase form749

12.4 Frequency-domain form750

12.5 Recursive running sum form750

12.6 Modified-sinc flter752

12.7 Realizations with reduced number of arithmetic operations753

12.7.1 Prefilter approach753

12.7.2 Interpolation approach756

12.7.3 Frequency-response masking approach760

12.7.4 Quadrature approach771

12.8 Do-it-yourself:efficient FIR structures776

12.9 Efficient FIR structures with MATLAB781

12.10 Summary782

12.11 Exercises782

13 Efficient IIR structures787

13.1 Introduction787

13.2 IIR parallel and cascade filters787

13.2.1 Parallel form788

13.2.2 Cascade form790

13.2.3 Error spectrum shaping795

13.2.4 Closed-form scaling797

13.3 State-space sections800

13.3.1 Optimal state-space sections801

13.3.2 State-space sections without limit cycles806

13.4 Lattice filters815

13.5 Doubly complementary filters822

13.5.1 QMF filter bank implementation826

13.6 Wave filters828

13.6.1 Motivation829

13.6.2 Wave elements832

13.6.3 Lattice wave digital filters848

13.7 Do-it-yourself:efficient IIR structures855

13.8 Efficient IIR structures with MATLAB857

13.9 Summary857

13.10 Exercises858

References863

Index877