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Discrete-time Signals 27 n = min(min(n1),min(n2)):max(max(n1),max(n2)); % duration of y(n) y1 = zeros(1,length(n)); y2 = y1; % y1(find((n>=min(n1))&(n=min(n2))&(n
28 Chapter 2 DISCRETE-TIME SIGNALS AND SYSTEMS 6. Sample summation: This operation differs from signal addition operation. It adds all sample values of x(n) between n 1 and n 2 . ∑n 2 n=n 1 x(n) =x(n 1 )+···+ x(n 2 ) It is implemented by the sum(x(n1:n2)) function. 7. Sample products: This operation also differs from signal multiplication operation. It multiplies all sample values of x(n) between n 1 and n 2 . ∏n 2 n 1 x(n) =x(n 1 ) ×···×x(n 2 ) It is implemented by the prod(x(n1:n2)) function. 8. Signal energy: The energy of a sequence x(n) isgiven by ∞∑ ∞∑ E x = x(n)x ∗ (n) = |x(n)| 2 −∞ where superscript ∗ denotes the operation of complex conjugation. 1 The energy of a finite-duration sequence x(n) can be computed in MATLAB using −∞ >> Ex = sum(x .* conj(x)); % one approach >> Ex = sum(abs(x) .^ 2); % another approach 9. Signal power: The average power of a periodic sequence ˜x(n) with fundamental period N is given by P x = 1 N N−1 ∑ 0 |˜x(n)| 2 □ EXAMPLE 2.1 Generate and plot each of the following sequences over the indicated interval. a. x(n) =2δ(n +2)− δ(n − 4), −5 ≤ n ≤ 5. b. x(n) =n[u(n)−u(n−10)]+10e −0.3(n−10) [u(n−10)−u(n−20)], 0 ≤ n ≤ 20. c. x(n) = cos(0.04πn) +0.2w(n), 0 ≤ n ≤ 50, where w(n) isaGaussian random sequence with zero mean and unit variance. d. ˜x(n) ={..., 5, 4, 3, 2, 1, 5, 4, 3, 2, 1, 5, 4, 3, 2, 1, ...}; −10 ≤ n ≤ 9. ↑ 1 The symbol * denotes many operations in digital signal processing. Its font (roman or computer) and its position (normal or superscript) will distinguish each operation. 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.
Page 2 and 3: Digital Signal Processing Using MAT
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 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
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The Frequency Domain Representation
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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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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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