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DSP First A Multimedia Approach

by: McClellan, James H.; Schafer, Ronald W.; Yoder, Mark A.

DSP First A Multimedia Approach

by: McClellan, James H.; Schafer, Ronald W.; Yoder, Mark A.

ISBN 13:
9780132431712
ISBN 10:
0132431718
Edition: 1st
Format: Hardcover
Copyright: 12/30/1997
Publisher: Prentice Hall
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Summary

This hands on, multi-media package provides a motivating introduction to fundamental concepts, specifically discrete-time systems, for beginning engineering readers. This class-tested learning package can also be used as a self-teaching tool for anyone eager to discover more about DSP applications, multi-media signals, and MATLAB.Presents basic DSP concepts in a clear and intuitive style. Integrated laboratory projects related to music, sound and image processing and new MATLAB functions for basic DSP operations are also included.Appropriate for readers interested in mastering fundamental concepts in today's electrical and computer engineering curriculum.

Preface

xvii

1 Introduction

(8)

1.1 Mathematical Representation of Signals

(3)

1.2 Mathematical Representation of Systems

(2)

1.3 Thinking About Systems

(1)

1.4 The Next Step

(1)

2 Sinusoids

(39)

2.1 An Experiment with a Tuning Fork

(2)

2.2 Review of Sine and Cosine Functions

(3)

2.3 Sinusoidal Signals

(5)

2.3.1 Relation of Frequency to Period

(1)

2.3.2 Relation of Phase Shift to Time Shift

(3)

2.4 Sampling and Plotting Sinusoids

(3)

2.5 Complex Exponentials and Phasors

(8)

2.5.1 Review of Complex Numbers

(2)

2.5.2 Complex Exponential Signals

(1)

2.5.3 The Rotating Phasor Interpretation

(3)

2.5.4 Inverse Euler Formulas

(2)

2.6 Phasor Addition

(6)

2.6.1 Addition of Complex Numbers

(1)

2.6.2 Phasor Addition Rule

(2)

2.6.3 Phasor Addition Rule: Example

(1)

2.6.4 MATLAB Demo of Phasors

(1)

2.6.5 Summary of the Phasor Addition Rule

(1)

2.7 Physics of the Tuning Fork

(4)

2.7.1 Equations from Laws of Physics

(3)

2.7.2 General Solution to the Differential Equation

(1)

2.7.3 Listening to Tones

(1)

2.8 Time Signals: More Than Formulas

(1)

2.9 Summary and Links

(1)

Problems

(5)

3 Spectrum Representation

(35)

3.1 The Spectrum of a Sum of Sinusoids

(3)

3.1.1 Graphical Plot of the Spectrum

(1)

3.2 Beat Notes

(6)

3.2.1 Multiplication of Sinusoids

(1)

3.2.2 Beat Note Waveform

(2)

3.2.3 Amplitude Modulation

(3)

3.3 Periodic Waveforms

(5)

3.3.1 Synthetic Vowel

(4)

3.4 More Periodic Signals

(6)

3.4.1 Fourier Series: Analysis

(1)

3.4.2 The Square Wave

(1)

3.4.3 Triangle Wave

(1)

3.4.4 Example of a Non-periodic Signal

(3)

3.5 Time-Frequency Spectrum

(5)

3.5.1 Stepped Frequency

(1)

3.5.2 Spectrogram Analysis

(1)

3.6 Frequency Modulation: Chirp Signals

(4)

3.6.1 Chirp, or Linearly Swept Frequency

(2)

3.6.2 A Closer Look at Instantaneous Frequency

(2)

3.7 Summary and Links

(1)

Problems

(5)

4 Sampling and Aliasing

(36)

4.1 Sampling

(7)

4.1.1 Sampling Sinusoidal Signals

(2)

4.1.2 The Sampling Theorem

(1)

4.1.3 Aliasing

(1)

4.1.4 Folding

(1)

4.2 Spectrum View of Sampling

(4)

4.2.1 Over-Sampling

(2)

4.2.2 Aliasing Due to Under-Sampling

(1)

4.2.3 Folding Due to Under-Sampling

(1)

4.2.4 Maximum Reconstructed Frequency

(1)

4.3 Strobe Demonstration

(6)

4.3.1 Spectrum Interpretation

(1)

4.4 Discrete-to-Continuous Conversion

100

(9)

4.4.1 Alias Frequencies Due to Sampling

101

(1)

4.4.2 Interpolation with Pulses

102

(1)

4.4.3 Zero-Order Hold Interpolation

103

(1)

4.4.4 Linear Interpolation

104

(1)

4.4.5 Parabolic Interpolation

105

(1)

4.4.6 Over-Sampling Aids Interpolation

106

(1)

4.4.7 Ideal Bandlimited Interpolation

107

(2)

4.5 The Sampling Theorem

109

(2)

4.6 Summary and Links

111

(1)

Problems

112

(7)

5 FIR Filters

119

(38)

5.1 Discrete-Time Systems

119

(2)

5.2 The Running Average Filter

121

(3)

5.3 The General FIR Filter

124

(9)

5.3.1 An Illustration of FIR Filtering

125

(2)

5.3.2 The Unit Impulse Response

127

(4)

5.3.2.1 Unit Impulse Sequence

128

(1)

5.3.2.2 Unit Impulse Response Sequence

129

(1)

5.3.2.3 The Unit-Delay System

130

(1)

5.3.3 Convolution and FIR Filters

131

(2)

5.3.3.1 Computing the Output of a Convolution

131

(2)

5.3.3.2 Convolution in MATLAB

133

(1)

5.4 Implementation of FIR Filters

133

(5)

5.4.1 Building Blocks

134

(1)

5.4.1.1 Multiplier

134

(1)

5.4.1.2 Adder

134

(1)

5.4.1.3 Unit Delay

135

(1)

5.4.2 Block Diagrams

135

(3)

5.4.2.1 Other Block Diagrams

136

(1)

5.4.2.2 Internal Hardware Details

137

(1)

5.5 Linear Time-Invariant (LTI) Systems

138

(4)

5.5.1 Time Invariance

139

(1)

5.5.2 Linearity

140

(1)

5.5.3 The FIR Case

141

(1)

5.6 Convolution and LTI Systems

142

(4)

5.6.1 Derivation of the Convolution Sum

142

(2)

5.6.2 Some Properties of LTI Systems

144

(2)

5.6.2.1 Convolution as an Operator

144

(1)

5.6.2.2 Commutative Property of Convolution

145

(1)

5.6.2.3 Associative Property of Convolution

146

(1)

5.7 Cascaded LTI Systems

146

(3)

5.8 Example of FIR Filtering

149

(3)

5.9 Summary and Links

152

(1)

Problems

152

(5)

6 Frequency Response of FIR Filters

157

(45)

6.1 Sinusoidal Response of FIR Systems

157

(3)

6.2 Superposition and the Frequency Response

160

(4)

6.3 Steady State and Transient Response

164

(2)

6.4 Properties of the Frequency Response

166

(3)

6.4.1 Relation to Impulse Response and Difference Equation

166

(2)

6.4.2 Periodicity of H (w)

168

(1)

6.4.3 Conjugate Symmetry

168

(1)

6.5 Graphical Representation of the Frequency Response

169

(7)

6.5.1 Delay System

170

(1)

6.5.2 First Difference System

170

(4)

6.5.3 A Simple Lowpass Filter

174

(2)

6.6 Cascaded LTI Systems

176

(3)

6.7 Running-Average Filtering

179

(9)

6.7.1 Plotting the Frequency Response

180

(4)

6.7.2 Cascade of Magnitude and Phase

184

(1)

6.7.3 Experiment: Smoothing an Image

184

(4)

6.8 Filtering Sampled Continuous-Time Signals

188

(6)

6.8.1 Example: Low-Pass Averager

190

(2)

6.8.2 Interpretation of Delay

192

(2)

6.9 Summary and Links

194

(1)

Problems

195

(7)

7 z-Transforms

202

(47)

7.1 Definition of the z-Transform

203

(2)

7.2 The z-Transform and Linear Systems

205

(3)

7.2.1 The z-Transform of an FIR Filter

205

(3)

7.3 Properties of the z-Transform

208

(3)

7.3.1 The Superposition Property of the z-Transform

208

(1)

7.3.2 The Time-Delay Property of the z-Transform

209

(1)

7.3.3 A General z-Transform Formula

210

(1)

7.4 The z-Transform as an Operator

211

(2)

7.4.1 Unit-Delay Operator

211

(1)

7.4.2 Operator Notation

212

(1)

7.4.3 Operator Notation in Block Diagrams

213

(1)

7.5 Convolution and the z-Transform

213

(7)

7.5.1 Cascading Systems

217

(1)

7.5.2 Factoring z-Polynomials

218

(1)

7.5.3 Deconvolution

219

(1)

7.6 Relationship Between the z-Domain and the w-Domain

220

(8)

7.6.1 The z-Plane and the Unit Circle

221

(1)

7.6.2 The Zeros and Poles of H(z)

222

(2)

7.6.3 Significance of the Zeros of H(z)

224

(1)

7.6.4 Nulling Filters

225

(1)

7.6.5 Graphical Relation Between z and w

226

(2)

7.7 Useful Filters

228

(8)

7.7.1 The L-Point Running Sum Filter

229

(2)

7.7.2 A Complex Bandpass Filter

231

(3)

7.7.3 A Bandpass Filter with Real Coefficients

234

(2)

7.8 Practical Bandpass Filter Design

236

(3)

7.9 Properties of Linear Phase Filters

239

(3)

7.9.1 The Linear Phase Condition

239

(2)

7.9.2 Locations of the Zeros of FIR Linear Phase Systems

241

(1)

7.10 Summary and Links

242

(1)

Problems

242

(7)

8 IIR Filters

249

(71)

8.1 The General IIR Difference Equation

250

(1)

8.2 Time-Domain Response

251

(10)

8.2.1 Linearity and Time Invariance of IIR Filters

254

(1)

8.2.2 Impulse Response of a First-Order IIR System

254

(2)

8.2.3 Response to Finite-Length Inputs

256

(2)

8.2.4 Step Response of a First-Order Recursive System

258

(3)

8.3 System Function of an IIR Filter

261

(8)

8.3.1 The General First-Order Case

261

(2)

8.3.2 The System Function and Block-Diagram Structures

263

(4)

8.3.2.1 Direct Form I Structure

263

(1)

8.3.2.2 Direct Form II Structure

264

(1)

8.3.2.3 The Transposed Form Structure

265

(2)

8.3.3 Relation to the Impulse Response

267

(1)

8.3.4 Summary of the Method

268

(1)

8.4 Poles and Zeros

269

(3)

8.4.1 Poles or Zeros at the Origin or Infinity

270

(1)

8.4.2 Pole Locations and Stability

271

(1)

8.5 Frequency Response of an IIR Filter

272

(6)

8.5.1 Frequency Response using MATLAB

274

(2)

8.5.2 Three-Dimensional Plot of a System Function

276

(2)

8.6 Three Domains

278

(1)

8.7 The Inverse z-Transform and Some Applications

279

(6)

8.7.1 Revisiting the Step Response of a First-Order System

280

(2)

8.7.2 A General Procedure for Inverse z-Transformation

282

(3)

8.8 Steady-State Response and Stability

285

(4)

8.9 Second-Order Filters

289

(13)

8.9.1 z-transform of Second-Order Filters

289

(2)

8.9.2 Structures for Second-Order IIR Systems

291

(2)

8.9.3 Poles and Zeros

293

(2)

8.9.4 Impulse Response of a Second-Order IIR System

295

(2)

8.9.4.1 Real Poles

296

(1)

8.9.5 Complex Poles

297

(5)

8.10 Frequency Response of Second-Order IIR Filter

302

(5)

8.10.1 Frequency Response via MATLAB

303

(2)

8.10.2 3-dB Bandwidth

305

(1)

8.10.3 Three-Dimensional Plot of System Functions

305

(2)

8.11 Example of an IIR Lowpass Filter

307

(3)

8.12 Summary and Links

310

(1)

Problems

311

(9)

9 Spectrum Analysis

320

(58)

9.1 Introduction and Review

321

(3)

9.1.1 Review of the Frequency Spectrum

321

(1)

9.1.2 A Spectrum Analyzer

322

(2)

9.2 Spectrum Analysis by Filtering

324

(4)

9.2.1 Frequency Shifting

324

(1)

9.2.2 Measuring the Average Value

325

(1)

9.2.3 Channel Filters

325

(3)

9.3 Spectrum Analysis of Periodic Signals

328

(12)

9.3.1 Periodic Signals

328

(1)

9.3.2 Spectrum of a Periodic Signal

329

(2)

9.3.3 Filtering with a Running Sum

331

(1)

9.3.4 Spectrum Analysis Using Running-Sum Filtering

331

(3)

9.3.5 The DFT: Discrete Fourier Transform

334

(2)

9.3.6 DFT Examples

336

(2)

9.3.7 The Fast Fourier Transform (FFT)

338

(2)

9.4 Spectrum Analysis of Sampled Periodic Signals

340

(3)

9.5 Spectrum Analysis of Nonperiodic Signals

343

(12)

9.5.1 Spectrum Analysis of Finite-Length Signals

344

(3)

9.5.2 Frequency Sampling

347

(2)

9.5.3 Samples of the Frequency Response

349

(2)

9.5.4 Spectrum Analysis of Continuing Nonperiodic Signals

351

(4)

9.6 The Spectrogram

355

(13)

9.6.1 Spectrograms in MATLAB

356

(1)

9.6.2 Spectrogram of a Sampled Periodic Signal

357

(2)

9.6.3 Resolution of the Spectrogram

359

(2)

9.6.3.1 Resolution Experiment

360

(1)

9.6.4 Spectrogram of a Musical Scale

361

(2)

9.6.5 Spectrogram of a Speech Signal

363

(5)

9.7 Filtered Speech

368

(3)

9.8 The Fast Fourier Transform (FFT)

371

(3)

9.8.1 Derivation of the FFT

371

(3)

9.8.1.1 FFT Operation Count

373

(1)

9.9 Summary and Links

374

(2)

Problems

376

(2)

Appendix A Complex Numbers

378

(21)

A.1 Introduction

379

(1)

A.2 Notation for Complex Numbers

380

(4)

A.2.1 Rectangular Form

380

(1)

A.2.2 Polar Form

381

(1)

A.2.3 Conversion: Rectangular and Polar

381

(2)

A.2.4 Difficulty in Second or Third Quadrant

383

(1)

A.3 Euler's Formula

384

(1)

A.3.1 Inverse Euler Formulas

385

(1)

A.4 Algebraic Rules for Complex Numbers

385

(3)

A.4.1 Exercises

388

(1)

A.5 Geometric Views of Complex Operations

388

(5)

A.5.1 Geometric View of Addition

389

(1)

A.5.2 Geometric View of Subtraction

390

(1)

A.5.3 Geometric View of Multiplication

391

(1)

A.5.4 Geometric View of Division

391

(1)

A.5.5 Geometric View of Inverse

392

(1)

A.5.6 Geometric View of Conjugate

393

(1)

A.6 Powers and Roots

393

(4)

A.6.1 Roots of Unity

394

(3)

A.6.1.1 Procedure for Finding Multiple Roots

395

(2)

A.7 Summary and Links

397

(1)

Problems

398

(1)

Appendix B Programming in MATLAB

399

(16)

B.1 MATLAB Help

400

(1)

B.2 Matrix Operations and Variables

400

(3)

B.2.1 The Colon Operator

401

(1)

B.2.2 Matrix and Array Operations

401

(2)

B.2.2.1 A Review of Matrix Multiplication

402

(1)

B.2.2.2 Pointwise Array Operations

403

(1)

B.3 Plots and Graphics

403

(2)

B.3.1 Figure Windows

404

(1)

B.3.2 Multiple Plots

404

(1)

B.3.3 Printing and Saving Graphics

405

(1)

B.4 Programming Constructs

405

(1)

B.4.1 MATLAB Built-in Functions

406

(1)

B.4.2 Program Flow

406

(1)

B.5 MATLAB Scripts

406

(1)

B.6 Writing a MATLAB Function

407

(3)

B.6.1 Creating A Clip Function

408

(2)

B.6.2 Debugging a MATLAB M-file

410

(1)

B.7 Programming Tips

410

(5)

B.7.1 Avoiding Loops

411

(1)

B.7.2 Repeating Rows or Columns

411

(1)

B.7.3 Vectorizing Logical Operations

412

(1)

B.7.4 Creating an Impulse

413

(1)

B.7.5 The Find Function

413

(1)

B.7.6 Seek to Vectorize

414

(1)

B.7.7 Programming Style

414

(1)

Appendix C Laboratory Projects

415

(93)

C.1 Laboratory: Introduction to MATLAB

417

(10)

C.1.1 Overview and Goals

417

(1)

C.1.2 Warm-up

417

(6)

C.1.2.1 Basic Commands

417

(2)

C.1.2.2 MATLAB Array Indexing

419

(1)

C.1.2.3 MATLAB Script Files

419

(1)

C.1.2.4 MATLAB Demos

420

(1)

C.1.2.5 MATLAB Sound

421

(1)

C.1.2.6 Functions

421

(2)

C.1.2.7 Vectorization

423

(1)

C.1.3 Exercises: Using MATLAB

423

(1)

C.1.3.1 Manipulating Sinusoids with MATLAB

424

(1)

C.1.4 Lab Review Questions

424

(3)

C.2 Laboratory: Introduction to Complex Exponentials

427

(6)

C.2.1 Overview

427

(2)

C.2.1.1 Complex Numbers in MATLAB

427

(1)

C.2.1.2 Sinusoid Addition Using Complex Exponentials

428

(1)

C.2.1.3 Harmonic Sinusoids

429

(1)

C.2.2 Warm-up

429

(1)

C.2.2.1 Complex Numbers

429

(1)

C.2.2.2 Sinusoidal Synthesis with an M-File

429

(1)

C.2.3 Exercises: Complex Exponentials

430

(2)

C.2.3.1 Representation of Sinusoids with Complex Exponentials

430

(1)

C.2.3.2 Verify Addition of Sinusoids Using Complex Exponentials

431

(1)

C.2.4 Periodic Waveforms

432

(1)

C.3 Laboratory: Synthesis of Sinusoidal Signals

433

(10)

C.3.1 Overview

433

(1)

C.3.2 Warm-up: Music Synthesis

433

(5)

C.3.2.1 D-to-A Conversion

434

(1)

C.3.2.2 Theory of Sampling

434

(1)

C.3.2.3 Piano Keyboard

435

(3)

C.3.3 Lab: Synthesis of Musical Notes

438

(4)

C.3.3.1 Spectrogram of the Music

439

(1)

C.3.3.2 Fur Elise

439

(1)

C.3.3.3 Musical Tweaks

440

(1)

C.3.3.4 Programming Tips

440

(1)

C.3.3.5 Alternative Piece: Jesu, Joy of Man's Desiring

441

(1)

C.3.3.6 Alternative Piece: Minuet in G

441

(1)

C.3.3.7 Alternative Piece: Beethoven's Fifth Symphony

441

(1)

C.3.3.8 Alternative Piece: Twinkle, Twinkle, Little Star

442

(1)

C.3.4 Sound Evaluation Criteria

442

(1)

C.4 Laboratory: AM and FM Sinusoidal Signals

443

(13)

C.4.1 Overview

443

(2)

C.4.1.1 Amplitude Modulation

443

(1)

C.4.1.2 Frequency Modulated Signals

443

(1)

C.4.1.3 Chirp, or Linearly Swept Frequency

444

(1)

C.4.1.4 Advanced Topic: Spectrograms

444

(1)

C.4.2 Warm-up

445

(1)

C.4.2.1 MATLAB Synthesis of Chirp Signals

445

(1)

C.4.3 Lab A: Chirps and Beats

446

(2)

C.4.3.1 Synthesize a Chirp

446

(1)

C.4.3.2 Beat Notes

446

(1)

C.4.3.3 More on Spectrograms (Optional)

447

(1)

C.4.4 Lab B: FM Synthesis of Instrument Sounds

448

(4)

C.4.4.1 Generating the Bell Envelopes

449

(1)

C.4.4.2 Parameters for the Bell

450

(1)

C.4.4.3 The Bell Sound

451

(1)

C.4.4.4 Comments about the Bell

452

(1)

C.4.5 Woodwinds

452

(4)

C.4.5.1 Generating the Envelopes for Woodwinds

452

(1)

C.4.5.2 Scaling the Clarinet Envelopes

453

(1)

C.4.5.3 Clarinet Envelopes

453

(1)

C.4.5.4 Parameters for the Clarinet

454

(1)

C.4.5.5 Experiment with the Clarinet Sound

455

(1)

C.5 Laboratory: FIR Filtering of Sinusoidal Waveforms

456

(7)

C.5.1 Overview of Filtering

456

(2)

C.5.1.1 Frequency Response of FIR Filters

457

(1)

C.5.2 Warm-up

458

(1)

C.5.2.1 Frequency Response of the 3-Point Averager

458

(1)

C.5.3 Lab: FIR Filters

459

(4)

C.5.3.1 Filtering Cosine Waves

459

(1)

C.5.3.2 First-Difference Filter

460

(1)

C.5.3.3 Linearity of the Filter

460

(1)

C.5.3.4 Time Invariance of the Filter

461

(1)

C.5.3.5 Cascading Two Systems

461

(2)

C.6 Laboratory: Filtering Sampled Waveforms

463

(6)

C.6.1 Overview of Linear Filters

463

(1)

C.6.2 Warm-up

464

(1)

C.6.2.1 Properties of Discrete-Time Filters

464

(1)

C.6.3 Laboratory: Sampling and Filters

465

(4)

C.6.3.1 Filtering a Stair-Step Signal

465

(1)

C.6.3.2 Implementation of Five-Point Averager

466

(1)

C.6.3.3 Implementation of First-Difference System

466

(1)

C.6.3.4 Implementation of First Cascade (Fig. C.11)

467

(1)

C.6.3.5 Implementation of Second Cascade (Fig. C.12)

467

(1)

C.6.3.6 Comparison of Systems of Figs. C.11 and C.12

467

(1)

C.6.3.7 Filtering the Speech Waveform

467

(2)

C.7 Laboratory: Everyday Sinusoidal Signals

469

(12)

C.7.1 Background

469

(5)

C.7.1.1 Background A: Telephone Touch Tone Dialing

469

(1)

C.7.1.2 DTMF Decoding

470

(1)

C.7.1.3 Background B: Amplitude Modulation (AM)

470

(2)

C.7.1.4 AM Demodulation

472

(1)

C.7.1.5 Envelope Detection (Peak Tracking)

472

(1)

C.7.1.6 LTI filter-based demodulation

473

(1)

C.7.1.7 Notch Filters for Demodulation

473

(1)

C.7.2 Warm-up A: DTMF Synthesis

474

(1)

C.7.2.1 DTMF Dial Function

474

(1)

C.7.3 Warm-up B: Tone Amplitude Modulation

475

(1)

C.7.4 Laboratory A: DTMF Decoding

475

(3)

C.7.4.1 Filter Design

475

(1)

C.7.4.2 A Scoring Function

476

(1)

C.7.4.3 DTMF Decode Function

477

(1)

C.7.4.4 Telephone Numbers

478

(1)

C.7.5 Laboratory B: AM Waveform Detection

478

(1)

C.7.6 Optional: Amplitude Modulation with Speech

479

(2)

C.8 Laboratory: Filtering and Edge Detection of Images

481

(11)

C.8.1 Overview

481

(2)

C.8.1.1 Digital Images

481

(1)

C.8.1.2 Displaying Images

481

(2)

C.8.1.3 Image Filtering

483

(1)

C.8.2 Warm-up: Display of Images

483

(1)

C.8.2.1 Display Test

484

(1)

C.8.3 Laboratory: Filtering Images

484

(8)

C.8.3.1 One-Dimensional Filtering

484

(1)

C.8.3.2 Blurring an Image

485

(1)

C.8.3.3 More Image Filters

486

(1)

C.8.3.4 Frequency Content of an Image

486

(2)

C.8.3.5 The Method of Synthetic Highs

488

(1)

C.8.3.6 Nonlinear Filters

489

(1)

C.8.3.7 Edges in an Image

489

(1)

C.8.3.8 The Slope-Threshold Function

490

(1)

C.8.3.9 What's Nonlinear about Edge Detection?

491

(1)

C.9 Laboratory: Sampling and Zooming of Images

492

(5)

C.9.1 Overview

492

(1)

C.9.2 Warm-up: Linear Interpolation

492

(1)

C.9.3 Laboratory: Sampling of Images

493

(4)

C.9.3.1 Reconstruction of Images

494

(1)

C.9.3.2 Zooming for an Image

495

(2)

C.10 Laboratory: The z-, n-, and w-Domains

497

(5)

C.10.1 Objective

497

(1)

C.10.2 Warm-up

497

(1)

C.10.3 Laboratory: Relationships Between z-, n-, and w-domains

497

(1)

C.10.4 Real Poles

498

(1)

C.10.5 Complex Poles

498

(1)

C.10.6 Filter Design

499

(3)

C.11 Laboratory: Extracting Frequencies of Musical Tones

502

(6)

C.11.1 Overview

502

(1)

C.11.2 Warm-up: System Components

502

(3)

C.11.2.1 Spectrogram Computation

502

(2)

C.11.2.2 Generating the Window

504

(1)

C.11.2.3 Display the Spectrogram

504

(1)

C.11.2.4 Finding Peaks

504

(1)

C.11.3 Design of the Music-Writing System

505

(2)

C.11.3.1 Block Diagram for the System

505

(1)

C.11.3.2 Write a Spectrogram Function

505

(1)

C.11.3.3 Parameters of the Spectrogram

506

(1)

C.11.3.4 Peak Picking and Editing

506

(1)

C.11.3.5 Writing the Musical Score

507

(1)

C.11.4 Testing the Music Extraction Program

507

(1)

Appendix D About the CD

508

(11)

Index

519

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DSP First A Multimedia Approach

DSP First A Multimedia Approach

9780132431712

0132431718

Summary

Table of Contents

Supplemental Materials

Write a Review

Amazon no longer offers textbook rentals. We do!

DSP First A Multimedia Approach

DSP First A Multimedia Approach

9780132431712

0132431718

Summary

Table of Contents

Supplemental Materials

Write a Review

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