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INDEX 647 optimal equiripple design, 368–377 plotting, 14–17 quantization noise analysis, 542–552, 569–576 rational factor I/D, 498–500, 519–520 reconstruction of signals, 92–97, 153 round-off effects, 542–552, 555–558, 569–576, 583–585, 588–589 sampling rate conversion, 480, 485–488, 489, 491–494, 498–500, 501–507, 512–514, 519–520 sampling signals, 84–87 scripts, 13 use of, 5–17 variables in, 7–8 windowing operations, 334–335 z-transform, 114–118, 120–125, 131–134 Matrix operations, MATLAB, 8–13 mean function, 548 Merging formula, 194 Minimizing approximation error (minimax) problem, 361–364 Minimum-phase filter, 391 Mirror-image symmetry, 391 Mixed-radix algorithm, FFT, 193 Moving average (MA) filters, 52 Multiple access code, 634 Multiple stopbands, sampling rate conversion, 521–522 Multiplication, 26–27, 69, 108, 180 DFT property, 180 by-a-ramp, 108 DTFT property, 69 signal operation, 26–27 z-transform property, 108 Multiplier (filter gain), 214 Multirate digital system processing systems, 476 Musical sound processing, 18 N N-point sequence, DFT, 154–165 Naïve design method, frequency sampling, 349–350 NaN function, 267 Narrowband interference, suppression of, 602–605 Natural frequencies, 48 Negative-time sequence, 105 Noise, 540–552, 565–580 A/D quantization, 540–552 round-off, 565–580 signal-to-noise ratio, 568–569, 572–574, 579–580 Nonperiodic signal, 153 Nonrecursive filters, 52 Normalized form, 264 Notch filters, 395–397 Null space, 104 Number representation, 6, 252–268 binary, 253–260, 265–266 decimals, 264 discrete-time filters, 252–268 excess-2 B−1 (biased) format, 260 fixed-point, 252–263 floating-point, 253, 263–268 IEEE 754 standard, 266–268 mantissa values, 264–267 MATLAB, 6, 254–258, 260, 267–268 one’s complement format, 253, 254–256, 262 real, 261–263 sign-magnitude format, 253, 254, 262 signed integers, 253–260 ten’s complement format, 258–260 two’s complement format, 253, 256–258, 260, 262 Number sequence, 22 Numerator polynomial, 105 Nyquist component, 169 Nyquist rate, 83 O oc2sm function, 263, 270 Omode function, 556 One-sided z-transform, 128–130 One’s complement number format, 253, 254–256, 262, 269–271 OnesComplement function, 256 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.
648 INDEX Operators, MATLAB, 8 Optimal equiripple design, 360–377 amplitude response, 361 Chebyshev approximation problem, 361, 364 extrema, 361, 365–367 FIR filter design, 360–377 MATLAB implementation, 368–377 minimizing approximation error (minimax) problem, 361–364 Parks-McClellan algorithm, 367–377 Optimum design method, frequency sampling, 350–360 Overflow limit cycles, 554, 560–562 Overlap-add convolution, 187 Overlap-save convolution, 185–187 ovrlpsav function, 186–187 P Parallel form, IIR filters, 222–229 parfiltr function, 224–225 Parks-McClellan algorithm, 367–377, 520 Parseval’s relation, DFT, 180 par2dir function, 225 Passband, 306–307 Periodic conjugate symmetry, DFS, 169 Periodic convolution, 69 Periodic sequence, 25, 142–143, 145–146 Periodic shifting, 172 Periodic-sinc function, 153 Periodicity in time and frequency, 33 Phase response, 75, 424–425 plot function, 94–95, 163 Plotting, MATLAB, 14–17 Pole-zero diagrams, 105 Pole-zero locations, quantization effects on, 275–282 poly function, 116 Polyphase structure, FIR sampling rate conversion, 522, 526–529 Positive-time sequence, 105 Power, signal operation, 28 Power spectrum, DFT, 180 prod function, 28 Prototype filters, 402–425, 450–463 analog, 402–425 digital, 450–463 Pseudo-noise (PN), 635–636 Pulse-code modulation (PCM), 609–613 Q Qcoeff function, 279–280 Qfix function, 557–562, 569–571, 575–576, 583–585 Qmode function, 556 Quantization, 268–290, 540–552, 562–580 A/D noise analysis, 540–552 digital filters, noise through, 549–550 error characteristics, 268–274, 540–552 filter coefficients, 275–290 FIR filters, 286–290 fixed-point arithmetic, 268–274, 565–569 floating-point arithmetic, 274 frequency response, effects on, 282–290 IIR filters, 275–286, 562–580 MATLAB analysis for, 542–547, 569–576 MATLAB implementation of, 548–549, 550–552 multiplication error, 562–580 noise, 540–552 pole-zero locations, effects on, 275–282 round-off effects, 540–552, 562–580 rounding operation, 268, 273–274, 547–548 statistical model of, 541–542, 547–548 truncation operation, 268–273, 547–548 R Radix-R algorithm, FFT, 193 Radix-2 algorithm, FFT, 193–195 rand function, 25 Random sequences, 25 Rational factor I/D, 495–500, 518–521 FIR filters, 518–521 MATLAB implementation, 498–500, 519–520 sampling rate conversion by, 495–500 Real number representation, 261–263 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.
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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.
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IIR Filter Structures 219 for i = 1
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IIR Filter Structures 221 6.2.6 PAR
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IIR Filter Structures 223 Brow = r(
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IIR Filter Structures 225 □ EXAMP
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IIR Filter Structures 227 a1 = 1.00
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FIR Filter Structures 229 FIGURE 6.
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FIR Filter Structures 235 6.3.8 MAT
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Lattice Filter Structures 239 1.000
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Lattice Filter Structures 241 There
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Lattice Filter Structures 243 FIGUR
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Lattice Filter Structures 245 FIGUR
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Lattice Filter Structures 247 funct
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Lattice Filter Structures 249 Solut
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Representation of Numbers 251 new f
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Representation of Numbers 253 rule
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Representation of Numbers 255 Solut
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Representation of Numbers 257 Ten
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Representation of Numbers 259 negat
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Representation of Numbers 261 Two
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Representation of Numbers 263 For t
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Representation of Numbers 265 IEEE
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The Process of Quantization and Err
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Quantization of Filter Coefficients
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Problems 289 z −1 x(n) K 2 2 0.5
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Problems 291 x(n) −1/2 1/2 −2/3
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Problems 293 0.5 1 −1 z −1 2 1
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Problems 295 1. Direct form 2. Line
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Problems 297 P6.24 MATLAB provides
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Problems 299 4. Explain why the mag
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Problems 301 P6.38 An IIR bandstop
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CHAPTER 7 FIR Filter Design We now
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Preliminaries 305 1 + δ 1 1 1 −
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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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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 668 and 669: INDEX 649 Real-valued exponential s
Page 670 and 671: INDEX 651 Sinusoidal signals, 83-84
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