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The Process of Quantization and Error Characterizations 269 1 0.75 x xhat 0.5 0.25 xhat 0 −0.25 −0.5 −0.75 FIGURE 6.26 −1 −1 −0.75 −0.5 −0.25 0 x 0.25 0.5 0.75 Truncation error characteristics in the one’s-complement format 1 Clearly, x is more negative than Q T [x] orx ≤Q T [x] ore T ≥ 0. In fact, the maximum truncation error is e Tmax =000 ···0111 ···=2 −B (decimal) Hence 0 ≤ e T ≤ 2 −B , for x
270 Chapter 6 IMPLEMENTATION OF DISCRETE-TIME FILTERS Two’s-complement format Once again, for x ≥ 0, we have −2 −B ≤ e T ≤ 0, for x ≥ 0 (6.52) For x
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Digital Signal Processing Using MAT
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Contents PREFACE xi 1 INTRODUCTION
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CONTENTS vii 6 IMPLEMENTATION OF DI
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CONTENTS ix 11.3 Suppression of Nar
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Preface From the beginning of the 1
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PREFACE xiii implementation. The di
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PREFACE xv ACKNOWLEDGMENTS We are i
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CHAPTER 1 Introduction During the p
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Overview of Digital Signal Processi
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A Brief Introduction to MATLAB 5 It
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A Brief Introduction to MATLAB 7 Va
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A Brief Introduction to MATLAB 9 us
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A Brief Introduction to MATLAB 11 o
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A Brief Introduction to MATLAB 13 o
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A Brief Introduction to MATLAB 15 T
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Applications of Digital Signal Proc
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Applications of Digital Signal Proc
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Brief Overview of the Book 21 In al
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Discrete-time Signals 23 In MATLAB
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Discrete-time Signals 25 For exampl
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Discrete-time Signals 27 n = min(mi
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Discrete-time Signals 29 Solution a
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Discrete-time Signals 31 Sequence i
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Discrete-time Signals 33 The quanti
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Discrete-time Signals 35 Rectangula
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Discrete Systems 37 In DSP we will
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Discrete Systems 39 every input seq
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Convolution 41 2 Input Sequence 1.5
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Convolution 43 x(k) and h(k) x(k) a
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Convolution 45 Hence y(n) ={6, 31,
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Difference Equations 47 Note that t
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Difference Equations 49 Solution Fr
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Difference Equations 51 8 Output Se
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Problems 53 IIR filter If the impul
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Problems 55 1. Modify the evenodd f
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Problems 57 2. x(n) ={1, 1, 0, 1, 1
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CHAPTER 3 The Discrete-time Fourier
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The Discrete-time Fourier Transform
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The Properties of the DTFT 67 TABLE
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The Properties of the DTFT 69 8. Mu
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The Properties of the DTFT 71 60 Ma
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The Properties of the DTFT 73 2 Rea
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The Frequency Domain Representation
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Sampling and Reconstruction of Anal
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Problems 97 % check >> error = max(
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Problems 99 Remember that the above
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Problems 101 P3.16 Foralinear, shif
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CHAPTER 4 The z-Transform In Chapte
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The Bilateral z-Transform 105 Im{z}
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Important Properties of the z-Trans
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Inversion of the z-Transform 113 wh
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Inversion of the z-Transform 115 be
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Inversion of the z-Transform 117 He
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System Representation in the z-Doma
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Solutions of the Difference Equatio
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Problems 135 4. x(n) =n 2 (2/3) n
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Problems 137 2. Using (4.32), deter
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Problems 139 It is also known that
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CHAPTER 5 The Discrete Fourier Tran
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The Discrete Fourier Series 143 den
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The Discrete Fourier Series 145 The
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The Discrete Fourier Series 147 DFS
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Sampling and Reconstruction in the
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The Discrete Fourier Transform 155
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Properties of the Discrete Fourier
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Linear Convolution Using the DFT 18
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The Fast Fourier Transform 187 5.6
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The Fast Fourier Transform 189 Usin
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The Fast Fourier Transform 191 and
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The Fast Fourier Transform 193 Fina
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The Fast Fourier Transform 195 Let
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The Fast Fourier Transform 197 N =2
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The Fast Fourier Transform 199 comp
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Problems 201 Clearly, ˜x 3(n) isdi
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Problems 203 determine the impulse
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Problems 205 and use this property.
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Problems 207 function x3 = circonvf
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Problems 209 where l is an integer.
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Problems 211 2. From the following
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Basic Elements 213 characteristics
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IIR Filter Structures 215 FIGURE 6.
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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 254 and 255: FIR Filter Structures 235 6.3.8 MAT
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 290 and 291: The Process of Quantization and Err
Page 292 and 293: Quantization of Filter Coefficients
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
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Properties of Linear-phase FIR Filt
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Properties of Linear-phase FIR Filt
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Window Design Techniques 323 where
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Window Design Techniques 325 Rectan
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Window Design Techniques 327 of att
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Window Design Techniques 329 Hammin
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Window Design Techniques 331 where
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Window Design Techniques 333 To dis
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Window Design Techniques 335 Ideal
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Window Design Techniques 337 Soluti
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Window Design Techniques 339 The id
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Window Design Techniques 341 □ EX
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Window Design Techniques 343 Ideal
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Frequency Sampling Design Technique
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Optimal Equiripple Design Technique
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Problems 375 h(n) 0.8 0.6 0.4 0.2 0
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Problems 377 where coefficients ˜c
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Problems 379 Plot the impulse respo
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Problems 381 2.02 1.98 Hr(ω) 1 0 0
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Problems 383 P7.34 Design a minimum
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Problems 385 P7.38 Design a minimum
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Some Preliminaries 387 8.1 SOME PRE
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Some Preliminaries 389 8.1.2 PROPER
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Some Special Filter Types 391 The c
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Some Special Filter Types 393 Magni
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Some Special Filter Types 395 Imagi
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Some Special Filter Types 397 (a) F
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Some Special Filter Types 399 circl
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Characteristics of Prototype Analog
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Analog-to-Digital Filter Transforma
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Lowpass Filter Design Using MATLAB
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Frequency-band Transformations 449
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Problems 461 1 0.8913 Magnitude Res
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Problems 463 1. Determine the value
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Problems 465 function [b,a] =afd(ty
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Problems 467 function [b,a] = mzt(c
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Problems 469 P8.35 Design a highpas
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Problems 471 Using this function, d
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Problems 473 1 0.9 Equiripple |H (e
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Introduction 475 x a (t) ADC F s =
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Decimation by a Factor D 477 as h(n
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Decimation by a Factor D 479 given
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Decimation by a Factor D 481 |X(ω
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Decimation by a Factor D 483 The ou
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Decimation by a Factor D 485 % (c)
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Interpolation by a Factor I 487 Sol
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Interpolation by a Factor I 489 Ide
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Interpolation by a Factor I 491 % (
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Sampling Rate Conversion by a Ratio
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FIR Filter Designs for Sampling Rat
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FIR Filter Structures for Sampling
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Problems 531 P9.3 Consider a signal
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Problems 533 1. Compute and plot th
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Problems 535 3. Let x(n) =cos(0.3π
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Problems 537 3. Using the fir2 func
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Analysis of A/D Quantization Noise
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Round-off Effects in IIR Digital Fi
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Round-off Effects in FIR Digital Fi
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Problems 591 P10.6 Consider the 1st
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Problems 593 which is implemented i
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Applications in Adaptive Filtering
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LMS Algorithm for Coefficient Adjus
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System Identification or System Mod
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Suppression of Narrowband Interfere
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Adaptive Channel Equalization 603 T
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Adaptive Channel Equalization 605 F
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CHAPTER 12 Applications in Communic
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Pulse-Code Modulation 609 called a
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Differential PCM (DPCM) 611 the sig
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Differential PCM (DPCM) 613 digits
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Adaptive PCM and DPCM (ADPCM) 615 a
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Adaptive PCM and DPCM (ADPCM) 617 F
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Delta Modulation (DM) 619 FIGURE 12
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Delta Modulation (DM) 621 FIGURE 12
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Linear Predictive Coding (LPC) of S
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Linear Predictive Coding (LPC) of S
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Dual-tone Multifrequency (DTMF) Sig
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Dual-tone Multifrequency (DTMF) Sig
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Binary Digital Communications 631 F
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Spread-Spectrum Communications 633
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BIBLIOGRAPHY [1] J. W. Cooley and J
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INDEX ’operator, 25 &operator, 26
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INDEX 639 adaptive delta modulation
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INDEX 641 finite-precision numerica
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INDEX 643 round-off effects, 580-59
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INDEX 645 DTFT formula, 152-153 err
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INDEX 647 optimal equiripple design
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INDEX 649 Real-valued exponential s
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INDEX 651 Sinusoidal signals, 83-84
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