UploadFile_6417

Recommendations

Info

Problems 97 % check >> error = max(abs(xa - exp(-1000*abs(t)))) error = 0.1679 The maximum error in this case is 0.1679, which is significant and cannot be attributed to the nonideal interpolation or nonband-limitedness of x a(t). From the bottom plot in Figure 3.19 observe that the reconstructed signal again differs from the actual one in many places over the interpolated regions. □ From these examples it is clear that for practical purposes the spline interpolation provides the best results. 3.5 PROBLEMS P3.1 Using the matrix-vector multiplication approach discussed in this chapter, write a MATLAB function to compute the DTFT of a finite-duration sequence. The format of the function should be function [X] = dtft(x,n,w) % Computes Discrete-time Fourier Transform % [X] = dtft(x,n,w) % X = DTFT values computed at w frequencies % x = finite duration sequence over n % n = sample position vector % w = frequency location vector Use this function to compute the DTFT X(e jω )ofthe following finite-duration sequences over −π ≤ ω ≤ π. Plot DTFT magnitude and angle graphs in one figure window. 1. x(n) =(0.6) |n| [u(n + 10) − u(n − 11)]. Comment on the angle plot. 2. x(n) =n(0.9) n [u(n) − u(n − 21)]. 3. x(n) =[cos(0.5πn)+j sin(0.5πn)][u(n) − u(n − 51)]. Comment on the magnitude plot. 4. x(n) ={4, 3, 2, 1, 1, 2, 3, 4}. Comment on the angle plot. ↑ 5. x(n) ={4, 3, 2, 1, −1, −2, −3, −4}. Comment on the angle plot. ↑ P3.2 Let x 1(n) ={1, 2, 2, 1}. Anew sequence x 2(n) isformed using ↑ { x1(n), 0 ≤ n ≤ 3; x 2(n) = x 1(n − 4), 4 ≤ n ≤ 7; 0, Otherwise. 1. Express X 2(e jω )interms of X 1(e jω ) without explicitly computing X 1(e jω ). 2. Verify your result using MATLAB by computing and plotting magnitudes of the respective DTFTs. (3.44) Copyright 2010 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.
98 Chapter 3 THE DISCRETE-TIME FOURIER ANALYSIS P3.3 Determine analytically the DTFT of each of the following sequences. Plot the magnitude and angle of X(e jω )over0≤ ω ≤ π. 1. x(n) =2(0.5) n u(n + 2). 2. x(n) =(0.6) |n| [u(n + 10) − u(n − 11)]. 3. x(n) =n (0.9) n u(n + 3). 4. x(n) =(n +3)(0.8) n−1 u(n − 2). 5. x(n) =4(−0.7) n cos(0.25πn)u(n). P3.4 The following finite-duration sequences are called windows and are very useful in DSP. { 1, 0 ≤ n
Page 2 and 3:
Digital Signal Processing Using MAT
Page 4 and 5:
Page 6 and 7:
Page 8 and 9:
Contents PREFACE xi 1 INTRODUCTION
Page 10 and 11:
CONTENTS vii 6 IMPLEMENTATION OF DI
Page 12 and 13:
CONTENTS ix 11.3 Suppression of Nar
Page 14 and 15:
Preface From the beginning of the 1
Page 16 and 17:
PREFACE xiii implementation. The di
Page 18 and 19:
PREFACE xv ACKNOWLEDGMENTS We are i
Page 20 and 21:
CHAPTER 1 Introduction During the p
Page 22 and 23:
Overview of Digital Signal Processi
Page 24 and 25:
A Brief Introduction to MATLAB 5 It
Page 26 and 27:
A Brief Introduction to MATLAB 7 Va
Page 28 and 29:
A Brief Introduction to MATLAB 9 us
Page 30 and 31:
A Brief Introduction to MATLAB 11 o
Page 32 and 33:
A Brief Introduction to MATLAB 13 o
Page 34 and 35:
A Brief Introduction to MATLAB 15 T
Page 36 and 37:
Applications of Digital Signal Proc
Page 38 and 39:
Applications of Digital Signal Proc
Page 40 and 41:
Brief Overview of the Book 21 In al
Page 42 and 43:
Discrete-time Signals 23 In MATLAB
Page 44 and 45:
Discrete-time Signals 25 For exampl
Page 46 and 47:
Discrete-time Signals 27 n = min(mi
Page 48 and 49:
Discrete-time Signals 29 Solution a
Page 50 and 51:
Discrete-time Signals 31 Sequence i
Page 52 and 53:
Discrete-time Signals 33 The quanti
Page 54 and 55:
Discrete-time Signals 35 Rectangula
Page 56 and 57:
Discrete Systems 37 In DSP we will
Page 58 and 59:
Discrete Systems 39 every input seq
Page 60 and 61:
Convolution 41 2 Input Sequence 1.5
Page 62 and 63:
Convolution 43 x(k) and h(k) x(k) a
Page 64 and 65:
Convolution 45 Hence y(n) ={6, 31,
Page 66 and 67: Difference Equations 47 Note that t
Page 68 and 69: Difference Equations 49 Solution Fr
Page 70 and 71: Difference Equations 51 8 Output Se
Page 72 and 73: Problems 53 IIR filter If the impul
Page 74 and 75: Problems 55 1. Modify the evenodd f
Page 76 and 77: Problems 57 2. x(n) ={1, 1, 0, 1, 1
Page 78 and 79: CHAPTER 3 The Discrete-time Fourier
Page 80 and 81: The Discrete-time Fourier Transform
Page 86 and 87: The Properties of the DTFT 67 TABLE
Page 88 and 89: The Properties of the DTFT 69 8. Mu
Page 90 and 91: The Properties of the DTFT 71 60 Ma
Page 92 and 93: The Properties of the DTFT 73 2 Rea
Page 94 and 95: The Frequency Domain Representation
Page 100 and 101: Sampling and Reconstruction of Anal
Page 118 and 119: Problems 99 Remember that the above
Page 120 and 121: Problems 101 P3.16 Foralinear, shif
Page 122 and 123: CHAPTER 4 The z-Transform In Chapte
Page 124 and 125: The Bilateral z-Transform 105 Im{z}
Page 126 and 127: Important Properties of the z-Trans
Page 132 and 133: Inversion of the z-Transform 113 wh
Page 134 and 135: Inversion of the z-Transform 115 be
Page 136 and 137: Inversion of the z-Transform 117 He
Page 138 and 139: System Representation in the z-Doma
Page 148 and 149: Solutions of the Difference Equatio
Page 154 and 155: Problems 135 4. x(n) =n 2 (2/3) n
Page 156 and 157: Problems 137 2. Using (4.32), deter
Page 158 and 159: Problems 139 It is also known that
Page 160 and 161: CHAPTER 5 The Discrete Fourier Tran
Page 162 and 163: The Discrete Fourier Series 143 den
Page 164 and 165: The Discrete Fourier Series 145 The
Page 166 and 167:
The Discrete Fourier Series 147 DFS
Page 168 and 169:
Sampling and Reconstruction in the
Page 170 and 171:
Page 172 and 173:
Page 174 and 175:
The Discrete Fourier Transform 155
Page 176 and 177:
Page 178 and 179:
Page 180 and 181:
Page 182 and 183:
Page 184 and 185:
Properties of the Discrete Fourier
Page 186 and 187:
Page 188 and 189:
Page 190 and 191:
Page 192 and 193:
Page 194 and 195:
Page 196 and 197:
Page 198 and 199:
Page 200 and 201:
Linear Convolution Using the DFT 18
Page 202 and 203:
Page 204 and 205:
Page 206 and 207:
The Fast Fourier Transform 187 5.6
Page 208 and 209:
The Fast Fourier Transform 189 Usin
Page 210 and 211:
The Fast Fourier Transform 191 and
Page 212 and 213:
The Fast Fourier Transform 193 Fina
Page 214 and 215:
The Fast Fourier Transform 195 Let
Page 216 and 217:
The Fast Fourier Transform 197 N =2
Page 218 and 219:
The Fast Fourier Transform 199 comp
Page 220 and 221:
Problems 201 Clearly, ˜x 3(n) isdi
Page 222 and 223:
Problems 203 determine the impulse
Page 224 and 225:
Problems 205 and use this property.
Page 226 and 227:
Problems 207 function x3 = circonvf
Page 228 and 229:
Problems 209 where l is an integer.
Page 230 and 231:
Problems 211 2. From the following
Page 232 and 233:
Basic Elements 213 characteristics
Page 234 and 235:
IIR Filter Structures 215 FIGURE 6.
Page 236 and 237:
IIR Filter Structures 217 FIGURE 6.
Page 238 and 239:
IIR Filter Structures 219 for i = 1
Page 240 and 241:
IIR Filter Structures 221 6.2.6 PAR
Page 242 and 243:
IIR Filter Structures 223 Brow = r(
Page 244 and 245:
IIR Filter Structures 225 □ EXAMP
Page 246 and 247:
IIR Filter Structures 227 a1 = 1.00
Page 248 and 249:
FIR Filter Structures 229 FIGURE 6.
Page 250 and 251:
Page 252 and 253:
Page 254 and 255:
FIR Filter Structures 235 6.3.8 MAT
Page 256 and 257:
Page 258 and 259:
Lattice Filter Structures 239 1.000
Page 260 and 261:
Lattice Filter Structures 241 There
Page 262 and 263:
Lattice Filter Structures 243 FIGUR
Page 264 and 265:
Lattice Filter Structures 245 FIGUR
Page 266 and 267:
Lattice Filter Structures 247 funct
Page 268 and 269:
Lattice Filter Structures 249 Solut
Page 270 and 271:
Representation of Numbers 251 new f
Page 272 and 273:
Representation of Numbers 253 rule
Page 274 and 275:
Representation of Numbers 255 Solut
Page 276 and 277:
Representation of Numbers 257 Ten
Page 278 and 279:
Representation of Numbers 259 negat
Page 280 and 281:
Representation of Numbers 261 Two
Page 282 and 283:
Representation of Numbers 263 For t
Page 284 and 285:
Representation of Numbers 265 IEEE
Page 286 and 287:
The Process of Quantization and Err
Page 288 and 289:
Page 290 and 291:
Page 292 and 293:
Quantization of Filter Coefficients
Page 294 and 295:
Page 296 and 297:
Page 298 and 299:
Page 300 and 301:
Page 302 and 303:
Page 304 and 305:
Page 306 and 307:
Page 308 and 309:
Problems 289 z −1 x(n) K 2 2 0.5
Page 310 and 311:
Problems 291 x(n) −1/2 1/2 −2/3
Page 312 and 313:
Problems 293 0.5 1 −1 z −1 2 1
Page 314 and 315:
Problems 295 1. Direct form 2. Line
Page 316 and 317:
Problems 297 P6.24 MATLAB provides
Page 318 and 319:
Problems 299 4. Explain why the mag
Page 320 and 321:
Problems 301 P6.38 An IIR bandstop
Page 322 and 323:
CHAPTER 7 FIR Filter Design We now
Page 324 and 325:
Preliminaries 305 1 + δ 1 1 1 −
Page 326 and 327:
Properties of Linear-phase FIR Filt
Page 328 and 329:
Page 330 and 331:
Page 332 and 333:
Page 334 and 335:
Page 336 and 337:
Page 338 and 339:
Page 340 and 341:
Page 342 and 343:
Window Design Techniques 323 where
Page 344 and 345:
Window Design Techniques 325 Rectan
Page 346 and 347:
Window Design Techniques 327 of att
Page 348 and 349:
Window Design Techniques 329 Hammin
Page 350 and 351:
Window Design Techniques 331 where
Page 352 and 353:
Window Design Techniques 333 To dis
Page 354 and 355:
Window Design Techniques 335 Ideal
Page 356 and 357:
Window Design Techniques 337 Soluti
Page 358 and 359:
Window Design Techniques 339 The id
Page 360 and 361:
Window Design Techniques 341 □ EX
Page 362 and 363:
Window Design Techniques 343 Ideal
Page 364 and 365:
Frequency Sampling Design Technique
Page 366 and 367:
Page 368 and 369:
Page 370 and 371:
Page 372 and 373:
Page 374 and 375:
Page 376 and 377:
Page 378 and 379:
Optimal Equiripple Design Technique
Page 380 and 381:
Page 382 and 383:
Page 384 and 385:
Page 386 and 387:
Page 388 and 389:
Page 390 and 391:
Page 392 and 393:
Page 394 and 395:
Problems 375 h(n) 0.8 0.6 0.4 0.2 0
Page 396 and 397:
Problems 377 where coefficients ˜c
Page 398 and 399:
Problems 379 Plot the impulse respo
Page 400 and 401:
Problems 381 2.02 1.98 Hr(ω) 1 0 0
Page 402 and 403:
Problems 383 P7.34 Design a minimum
Page 404 and 405:
Problems 385 P7.38 Design a minimum
Page 406 and 407:
Some Preliminaries 387 8.1 SOME PRE
Page 408 and 409:
Some Preliminaries 389 8.1.2 PROPER
Page 410 and 411:
Some Special Filter Types 391 The c
Page 412 and 413:
Some Special Filter Types 393 Magni
Page 414 and 415:
Some Special Filter Types 395 Imagi
Page 416 and 417:
Some Special Filter Types 397 (a) F
Page 418 and 419:
Some Special Filter Types 399 circl
Page 420 and 421:
Characteristics of Prototype Analog
Page 422 and 423:
Page 424 and 425:
Page 426 and 427:
Page 428 and 429:
Page 430 and 431:
Page 432 and 433:
Page 434 and 435:
Page 436 and 437:
Page 438 and 439:
Page 440 and 441:
Page 442 and 443:
Analog-to-Digital Filter Transforma
Page 444 and 445:
Page 446 and 447:
Page 448 and 449:
Page 450 and 451:
Page 452 and 453:
Page 454 and 455:
Page 456 and 457:
Page 458 and 459:
Page 460 and 461:
Page 462 and 463:
Lowpass Filter Design Using MATLAB
Page 464 and 465:
Page 466 and 467:
Page 468 and 469:
Frequency-band Transformations 449
Page 470 and 471:
Page 472 and 473:
Page 474 and 475:
Page 476 and 477:
Page 478 and 479:
Page 480 and 481:
Problems 461 1 0.8913 Magnitude Res
Page 482 and 483:
Problems 463 1. Determine the value
Page 484 and 485:
Problems 465 function [b,a] =afd(ty
Page 486 and 487:
Problems 467 function [b,a] = mzt(c
Page 488 and 489:
Problems 469 P8.35 Design a highpas
Page 490 and 491:
Problems 471 Using this function, d
Page 492 and 493:
Problems 473 1 0.9 Equiripple |H (e
Page 494 and 495:
Introduction 475 x a (t) ADC F s =
Page 496 and 497:
Decimation by a Factor D 477 as h(n
Page 498 and 499:
Decimation by a Factor D 479 given
Page 500 and 501:
Decimation by a Factor D 481 |X(ω
Page 502 and 503:
Decimation by a Factor D 483 The ou
Page 504 and 505:
Decimation by a Factor D 485 % (c)
Page 506 and 507:
Interpolation by a Factor I 487 Sol
Page 508 and 509:
Interpolation by a Factor I 489 Ide
Page 510 and 511:
Interpolation by a Factor I 491 % (
Page 512 and 513:
Sampling Rate Conversion by a Ratio
Page 514 and 515:
Page 516 and 517:
Page 518 and 519:
FIR Filter Designs for Sampling Rat
Page 520 and 521:
Page 522 and 523:
Page 524 and 525:
Page 526 and 527:
Page 528 and 529:
Page 530 and 531:
Page 532 and 533:
Page 534 and 535:
Page 536 and 537:
Page 538 and 539:
Page 540 and 541:
FIR Filter Structures for Sampling
Page 542 and 543:
Page 544 and 545:
Page 546 and 547:
Page 548 and 549:
Page 550 and 551:
Problems 531 P9.3 Consider a signal
Page 552 and 553:
Problems 533 1. Compute and plot th
Page 554 and 555:
Problems 535 3. Let x(n) =cos(0.3π
Page 556 and 557:
Problems 537 3. Using the fir2 func
Page 558 and 559:
Analysis of A/D Quantization Noise
Page 560 and 561:
Page 562 and 563:
Page 564 and 565:
Page 566 and 567:
Page 568 and 569:
Page 570 and 571:
Round-off Effects in IIR Digital Fi
Page 572 and 573:
Page 574 and 575:
Page 576 and 577:
Page 578 and 579:
Page 580 and 581:
Page 582 and 583:
Page 584 and 585:
Page 586 and 587:
Page 588 and 589:
Page 590 and 591:
Page 592 and 593:
Page 594 and 595:
Page 596 and 597:
Page 598 and 599:
Round-off Effects in FIR Digital Fi
Page 600 and 601:
Page 602 and 603:
Page 604 and 605:
Page 606 and 607:
Page 608 and 609:
Page 610 and 611:
Problems 591 P10.6 Consider the 1st
Page 612 and 613:
Problems 593 which is implemented i
Page 614 and 615:
Applications in Adaptive Filtering
Page 616 and 617:
LMS Algorithm for Coefficient Adjus
Page 618 and 619:
System Identification or System Mod
Page 620 and 621:
Suppression of Narrowband Interfere
Page 622 and 623:
Adaptive Channel Equalization 603 T
Page 624 and 625:
Adaptive Channel Equalization 605 F
Page 626 and 627:
CHAPTER 12 Applications in Communic
Page 628 and 629:
Pulse-Code Modulation 609 called a
Page 630 and 631:
Differential PCM (DPCM) 611 the sig
Page 632 and 633:
Differential PCM (DPCM) 613 digits
Page 634 and 635:
Adaptive PCM and DPCM (ADPCM) 615 a
Page 636 and 637:
Adaptive PCM and DPCM (ADPCM) 617 F
Page 638 and 639:
Delta Modulation (DM) 619 FIGURE 12
Page 640 and 641:
Delta Modulation (DM) 621 FIGURE 12
Page 642 and 643:
Linear Predictive Coding (LPC) of S
Page 644 and 645:
Linear Predictive Coding (LPC) of S
Page 646 and 647:
Dual-tone Multifrequency (DTMF) Sig
Page 648 and 649:
Dual-tone Multifrequency (DTMF) Sig
Page 650 and 651:
Binary Digital Communications 631 F
Page 652 and 653:
Spread-Spectrum Communications 633
Page 654 and 655:
BIBLIOGRAPHY [1] J. W. Cooley and J
Page 656 and 657:
INDEX ’operator, 25 &operator, 26
Page 658 and 659:
INDEX 639 adaptive delta modulation
Page 660 and 661:
INDEX 641 finite-precision numerica
Page 662 and 663:
INDEX 643 round-off effects, 580-59
Page 664 and 665:
INDEX 645 DTFT formula, 152-153 err
Page 666 and 667:
INDEX 647 optimal equiripple design
Page 668 and 669:
INDEX 649 Real-valued exponential s
Page 670 and 671:
INDEX 651 Sinusoidal signals, 83-84
show all

UploadFile_6417

Create successful ePaper yourself

Delete template?

Save as template?