Digital Signal Processing

, by Roberts, Richard A.; Mullis, Clifford T.

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ISBN: 9780201163506 | 0201163500
Cover: Paperback
Copyright: 2/1/1987

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Disucsses the theory associated with the processing of digital signals, including new material on implementation details of digital filters. For advanced level students in electrical engineering and for computer and electrical engineering professionals.

Preface

iii

Digital Signal Processing

(4)

Introduction

(1)

An Outline of the Book

(3)

Discrete-Time Signals and Systems

(48)

Introduction

(2)

Discrete-Time Signals

(1)

Discrete-Time Systems

(3)

The Unit-Pulse Response Characterization of LSI Systems

(7)

Convolution and the Unit-Pulse Response Sequence

(1)

Properties of the Unit-Pulse Response

(3)

Deconvolution

(1)

Characterization of BIBO Stability

(1)

The Frequency Response Function

(13)

Computation of the Frequency Response Function

(8)

The Standard Difference Equation

(11)

Solving the SDE

(1)

Characterization of All Solutions to the HE

(1)

Choosing the Constants of the Homogeneous Solution

(2)

The Unit-Pulse Response from the SDE

(3)

The Frequency Response Function from the SDE

(1)

Stability

(1)

Signal Flow Graphs

(3)

A Hierarchy of Discrete-Time System Descriptions

(8)

Problems

(6)

The z-Transform

(32)

The Bilateral z-Transform

(3)

Properties of the z-Transform

(6)

Linearity

(1)

Shifting

(1)

Convolution

(1)

Scaling

(1)

Multiplication by k

(2)

Vector Sequences

(1)

Inversion of the z-Transform

(6)

Direct Division

(1)

Partial Fraction Expansions

(2)

The Inversion Integral

(3)

The z-Transform of the Product fg and Parseval's Theorem

(1)

Inversion of z-Transforms, Causality, and BIBO Stability

(2)

Frequency Response and H(z)

(1)

Structural Forms of H(z)

(13)

FIR Lattice Structures

(3)

Problems

(6)

Fourier Analysis of Discrete-Time Signals and Systems

(62)

Introduction

(2)

The Discrete-Time Fourier Transform

(12)

Orthogonality Properties

(2)

Shift Properties

(5)

Symmetry Properties

(2)

Fourier Series

(2)

The Fourier Transform

101

(4)

The Discrete Fourier Transform

105

(7)

Orthogonality Properties of the DFT

107

(1)

Shift Properties of the DFT

108

(4)

Sampling and Generalized Convolution

112

(13)

Sampling and Aliasing

113

(7)

Generalized Convolution-Multiplication

120

(5)

Generalized Multiplication-Convolution

125

(1)

Equivalent Analog Filters and the Sampling Theorem

125

(5)

Equivalent Analog Filtering

126

(1)

The Shannon Sampling Theorem

127

(2)

Practical Reconstruction

129

(1)

The DFT Approximation to the Fourier Transform

130

(6)

Choosing to and N

133

(3)

FIR Filter Implementation Based on the DFT

136

(11)

Problems

139

(8)

Fast Algorithms for the Discrete Fourier Transform

147

(26)

Introduction

147

(1)

Power-of-2 FFT Algorithms

148

(4)

Other Forms of the FFT

152

(4)

Bit Reversal Permutation

154

(1)

Other Permutations and the FFT

154

(2)

Algorithms for the Inverse DFT

156

(1)

More Fast Algorithms

156

(4)

Prime Factor and Related Algorithms

160

(3)

A Fast Algorithm by Good

162

(1)

Reduced Multiplier FFT Algorithms

163

(1)

Fast Algorithms for Aperiodic Convolution of Two Finite Sequences.

164

(2)

Additional Comments on the Use of the FFT

166

(7)

Digital Filtering of Real Signals

168

(1)

Problems

169

(4)

The Approximation Problem for Digital Filters

173

(56)

Introduction

173

(2)

Finite-Impulse Response or Nonrecursive Filter Design

175

(2)

Linear Phase FIR Filters

176

(1)

Window Design of FIR Filters

177

(11)

Other Window Functions

183

(5)

FIR Filter Design by Frequency Sampling

188

(3)

Minimax Design of FIR Filters

191

(2)

The Approximation Problem for IIR Digital Filters

193

(9)

Impulse Invariance

194

(4)

The Bilinear Transform Method

198

(4)

The Matched z-Transformation Design

202

(1)

A Minimum Mean Squared Error Design

202

(1)

Frequency Transformations

202

(5)

A Comparison of FIR and IIR Digital Filters

207

(22)

Problems

208

(9)

Appendix 6A Design of Analog Low-Pass Filter Prototypes

217

(1)

Butterworth Filters

218

(2)

Chebyshev Filters

220

(1)

Inverse Chebyshev Filters

221

(1)

Elliptic Filters

222

(3)

Appendix 6B The Chebyshev Window Function

225

(4)

Least-Squares Filter Design

229

(58)

Introduction

229

(1)

Deterministic Least Squares

230

(13)

The FIR Whitening Problem

236

(4)

Asymptotic Behavior (n → ∞)

240

(3)

Wide Sense Stationary Signals

243

(9)

White Noise

244

(4)

The Wiener-Khintchine Theorem

248

(2)

The Signal Modeling Problem (Spectral Factorization)

250

(2)

Statistical Least Squares

252

(15)

The Noncausal Case

255

(1)

The FIR Case

256

(5)

The Causal IIR Case

261

(6)

Adaptive Filters

267

(20)

The Widrow Algorithm

268

(6)

Problems

274

(7)

Appendix 7A Quadratic Forms

281

(2)

Decomposition of Quadratic Forms

283

(4)

Internal Descriptions for Digital Filters

287

(56)

Introduction

287

(3)

The Reasons for More Detailed Filter Descriptions

290

(1)

Primitive Signal Flow Graphs

290

(7)

Definition

291

(1)

Node Ordering Procedure

291

(6)

State Variable Descriptions

297

(10)

State Variable Description from a PSFG

297

(3)

Transfer Function from the State Variable Description

300

(1)

Standard Difference Equation from the State Variable Description

301

(1)

Time Domain State Variable Descriptions

301

(2)

Unit-Pulse Response from the State Variable Description

303

(1)

Coordinate Transformations

304

(1)

Poles and Zeros and the State Variable Description

305

(2)

Factored State Variable Descriptions

307

(9)

Construction of the Factored State Variable Description

307

(1)

Examples of FSVDs

308

(5)

Primitive Signal Flow Graphs with Fractional Delays

313

(3)

Node Ordering for Fractional Delay PSFGs

316

(1)

State Variable Descriptions and Wide Sense Stationary Inputs

316

(27)

Calculation of the Output Autocorrelation Function in Terms of (A,B,C,D)

319

(1)

The Matrix K and Liapunov Stability

320

(2)

Factored State Variable Equations

322

(1)

Problems

323

(8)

Appendix 8A Special Representation and Functions of a Matrix

331

(8)

Eigenvectors

339

(1)

Transformations

339

(1)

Normal Matrices

340

(3)

Finite Length Register Effects in Fixed Point Digital Filters

343

(84)

Introduction

343

(1)

Analog-to-Digital Conversion and Quantization Noise

344

(4)

Limit Cycles--Overflow Oscillations

348

(6)

A State Variable Model for Overflow

350

(4)

Filter Structures Free of Overflow Oscillations

354

(6)

Summary on Overflow Limit Cycles

359

(1)

Roundoff Noise in IIR Digital Filters

360

(4)

Computation of Output Roundoff Noise

361

(3)

Scaling Fixed Point Digital Filters to Prevent Overflow

364

(7)

Scaling Rules

365

(1)

The Scaling Operation

366

(1)

Scaling State Variable Descriptions

366

(5)

The Tradeoff Between Overflow and Roundoff Noise

371

(6)

Reachable Sets: A Geometrical Interpretation of Scaling

377

(8)

Geometry of Error Ellipsoids

384

(1)

The Synthesis of Minimum Roundoff Noise State Variable Filters

385

(4)

The Optimal (Unequal) Word Length (OWL) Case

386

(1)

The Equal Word Length (EWL) Case

387

(1)

Minimization of the Geometric Mean of Kii Wii

387

(1)

Minimization of the Arithmetic Mean of Kii Wii

388

(1)

Properties of Minimum Roundoff Noise Structures

389

(3)

Frequency Transformations of Minimum Roundoff Noise Filters

390

(1)

State Variable and Nonstate Variable Nodes

391

(1)

Computation of K and W

392

(1)

Sectional Optimal Structures

393

(5)

Normal Form (Unscaled)

396

(2)

Noise Gain Formulas for Second-Order Minimum Noise Filters

398

(2)

Block Optimal Structures

400

(2)

An Example

402

(5)

Sectional Optimal Design

405

(2)

Coefficient Sensitivity of Digital Filters

407

(3)

Coefficient Quantization Effects Measured by Pole-Zero Movement

409

(1)

The Deadband Effect: Constant Input Limit Cycles

410

(17)

Problems

417

(10)

Digital Processing Structures

427

(56)

Introduction

427

(6)

Hardware Implementations for a Sum of Products

429

(4)

Block Processing Digital Filters

433

(7)

Hardware Considerations

438

(2)

Summary

440

(1)

Multirate Digital Filters

440

(9)

Decimation

440

(7)

Interpolator Structures

447

(2)

Orthogonal Filter Structures

449

(34)

Characterization of Orthogonal Filter Structures

451

(1)

Orthogonal All-Pass Filters

452

(2)

Examples of Filters in J0

454

(1)

Connections of Orthogonal, All-Pass Filters

455

(3)

Decomposition of Orthogonal, All-Pass Filters into Primitives

458

(6)

Processor Modules for Width Two Realizations

464

(1)

Synthesis of Orthogonal Filters--General Case

464

(5)

Overflow Oscillations

469

(1)

Noise Gain

470

(1)

Problems

471

(9)

Appendix 10A Orthogonal Matrices and All-Pass Filters

480

(3)

Spectral Estimation

483

(76)

Introduction to Spectral Estimation

483

(11)

Energy Spectral Density (ESD)

484

(1)

Power Spectral Density (PSD)

484

(4)

Approaches to Spectral Estimation

488

(1)

Estimation Using the ESD

489

(1)

Indirect Estimation from Autocorrelation Values

489

(1)

Sinusoidal Data Fitting

490

(1)

Whitening the Data (Analysis/Synthesis)

491

(2)

Issues

493

(1)

The Periodogram and MA Spectra

494

(12)

Bias

495

(6)

Variance

501

(2)

Bias versus Variance

503

(1)

Welch's Method

504

(1)

Use of the Fast Fourier Transform

505

(1)

Autoregressive Models

506

(40)

Whitening and Prediction Problems

508

(8)

Theoretical Issues Relating Analysis and Synthesis Cases

516

(4)

Lattices and the Levinson Algorithm

520

(4)

The Lattice Form of the Levinson Algorithm

524

(1)

Inverting the Levinson Algorithm

525

(3)

The Burg Spectral Estimator

528

(4)

Coding Spectra with Reflection Coefficients

532

(1)

The Singular Case and Line Spectra

533

(2)

The Pisarenko Model

535

(3)

Singular Value Decomposition and Sensitivity

538

(4)

The Maximum Entropy Property

542

(2)

A Classification of Spectra

544

(2)

ARMA Spectra and an Analysis/Synthesis Point of View

546

(13)

Analysis

547

(1)

Synthesis

548

(1)

Extension Problem

548

(1)

Application

549

(1)

Problems

550

(9)

References

559

(8)

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Digital Signal Processing

Summary

Table of Contents

Supplemental Materials

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