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ANSWERS TO SELECTED PROBLEMS NOTE: Detailed solutions for all problems listed below are given in the Student Solutions Manual that is available for free downloading from www.pearsonhighered.com/couch. or www.lcouch.us. Also, MATLAB solution files, downloaded from these same Web sites, are available for the problems listed below that have computer solutions. Chapter 1 1–3 See Student Solutions Manual 1–6 1.97 bits 1–9 (a) 0.5 (b) 1 bit Also, see MATLAB file P1_09.m 1–10 H = 3.084 bits 1–12 H = 3.32 bits, T = 1.11 s 1–15 (a) 7 bits (b) 3,044 characters/sec Also, see MATLAB file P1_15.m 1–18 [1 1 0 1 1 0 0 1 1 1] Also, see MATLAB file P1_18.m 739
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Abbreviations AC ADC ADM AM ANSI AP
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DIGITAL AND ANALOG COMMUNICATION SY
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CONTENTS PREFACE LIST OF SYMBOLS xi
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Contents v 2-8 Discrete Fourier Tra
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Contents vii 4-16 Transmitters and
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Contents ix 6-10 Appendix: Proof of
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Contents xi 8-11 Wireless Data Netw
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PREFACE Continuing the tradition of
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Preface xv THE PRACTICAL APPLICATIO
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LIST OF SYMBOLS There are not enoug
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List of Symbols xix l an integer n
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List of Symbols xxi DEFINED FUNCTIO
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C h a p t e r INTRODUCTION CHAPTER
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Sec. 1-1 Historical Perspective 3 s
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Sec. 1-2 Digital and Analog Sources
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Sec. 1-4 Organization of the Book 7
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Sec. 1-6 Block Diagram of a Communi
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Sec. 1-7 Frequency Allocations 11 T
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Sec. 1-8 Propagation of Electromagn
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Sec. 1-8 Propagation of Electromagn
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Sec. 1-9 Information Measure 17 In
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Sec. 1-10 Channel Capacity and Idea
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Sec. 1-11 Coding 21 Transmitter Noi
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Sec. 1-11 Coding 23 Convolutional C
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Sec. 1-11 Coding 25 0 1 0 (00) Path
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Sec. 1-11 Coding 27 10 -1 P e = Pro
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Sec. 1-11 Coding 29 TABLE 1-4 CODIN
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Problems 31 Solution: Using Eq. (1-
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Problems 33 1-17 Using the definiti
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Sec. 2-1 Properties of Signals and
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Sec. 2-2 Fourier Transform and Spec
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( ( Sec. 2-2 Fourier Transform and
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` Sec. 2-2 Fourier Transform and Sp
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Sec. 2-3 Power Spectral Density and
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Sec. 2-3 Power Spectral Density and
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Sec. 2-4 Orthogonal Series Represen
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Sec. 2-4 Orthogonal Series Represen
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Sec. 2-5 Fourier Series 71 2-5 FOUR
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Sec. 2-5 Fourier Series 73 where th
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Sec. 2-5 Fourier Series 75 Imaginar
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Sec. 2-5 Fourier Series 77 But the
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Sec. 2-5 Fourier Series 79 The spec
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Sec. 2-5 Fourier Series 81 The PSD
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Sec. 2-6 Review of Linear Systems 8
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Sec. 2-7 Bandlimited Signals and No
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Sec. 2-8 Discrete Fourier Transform
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Sec. 2-9 Bandwidth of Signals 105 N
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Sec. 2-9 Bandwidth of Signals 107 m
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Sec. 2-9 Bandwidth of Signals 109 m
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Sec. 2-9 Bandwidth of Signals 111 w
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Sec. 2-11 Study-Aid Examples 113 2-
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Sec. 2-11 Study-Aid Examples 115 SA
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Problems 117 b. Given the RC low-pa
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Problems 119 Sinusoidal current sou
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Problems 121 w(t) A -t 2 -t 1 t 1 t
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Problems 123 where A 1 , A 2 , v1,
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Problems 125 2-57 Show that the qua
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Problems 127 ★ 2-70 Assume that v
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ƒ ƒ Problems 129 2-82 The signal
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Problems 131 2-97 Given the low-pas
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Sec. 3-2 Pulse Amplitude Modulation
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Sec. 3-3 Pulse Code Modulation 141
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PCM transmitter (analog-to-digital
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Sec. 3-4 Digital Signaling 155 wher
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Sec. 3-4 Digital Signaling 157 Eq.
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Q Sec. 3-4 Digital Signaling 159 s(
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Sec. 3-4 Digital Signaling 161 1.5
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Sec. 3-4 Digital Signaling 163 Bina
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Sec. 3-5 Line Codes and Spectra 165
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Sec. 3-6 Intersymbol Interference 1
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Sec. 3-7 Differential Pulse Code Mo
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DPCM transmitter Analog input signa
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Sec. 3-8 Delta Modulation 199 DM tr
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Sec. 3-8 Delta Modulation 201 Granu
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Sec. 3-8 Delta Modulation 203 This
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Analog input signal Low-pass filter
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Analog input signals Channel 1 (fro
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Low-level distorted TDM input Ampli
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Sec. 3-9 Time-Division Multiplexing
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1 1 1 1 1 30 digital inputs, 64 kb/
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Sec. 3-10 Packet Transmission Syste
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Sec. 3-11 Pulse Time Modulation: Pu
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Sec. 3-11 Pulse Time Modulation: Pu
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Sec. 3-13 Study-Aid Examples 225 (a
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Sec. 3-13 Study-Aid Examples 227 (d
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Problems 229 ★ 3-7 Assume that an
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Problems 231 How does the PSD for t
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Problems 233 (a) Using a PC, calcul
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Problems 235 and w 3 (t) = -(t - 1)
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C h a p t e r BANDPASS SIGNALING PR
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Sec. 4-1 Complex Envelope Represent
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Sec. 4-3 Spectrum of Bandpass Signa
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AM A c |1+m(t2| e 0, m (t) 7-1 L c
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Sec. 4-4 Evaluation of Power 245 Re
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Sec. 4-4 Evaluation of Power 247 wh
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Sec. 4-5 Bandpass Filtering and Lin
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Sec. 4-5 Bandpass Filtering and Lin
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Sec. 4-6 Bandpass Sampling Theorem
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Sec. 4-8 Classification of Filters
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Sec. 4-8 Classification of Filters
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Sec. 4-9 Nonlinear Distortion 259 T
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Sec. 4-9 Nonlinear Distortion 261 t
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Sec. 4-9 Nonlinear Distortion 263 w
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Sec. 4-10 Limiters 265 v out Ideal
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Sec. 4-11 Mixers, Up Converters, an
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Sec. 4-12 Frequency Multipliers 273
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Sec. 4-13 Detector Circuits 275 the
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Sec. 4-13 Detector Circuits 277 Det
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Sec. 4-13 Detector Circuits 279 Fre
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Sec. 4-13 Detector Circuits 281 Thi
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Sec. 4-14 Phase-Locked Loops and Fr
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Sec. 4-16 Transmitters and Receiver
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Sec. 4-17 Software Radios 297 Zero-
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Sec. 4-19 Study-Aid Examples 301 No
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Sec. 4-19 Study-Aid Examples 303 Th
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PROBLEMS Problems 305 4-1 Show that
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Problems 307 where m(t) is the modu
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Problems 309 Assume that the input
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Problems 311 4-39 Rework Prob. 4-38
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C h a p t e r AM, FM, AND DIGITAL M
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Sec. 5-1 Amplitude Modulation 315 m
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Sec. 5-1 Amplitude Modulation 317 v
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Sec. 5-2 AM Broadcast Technical Sta
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Sec. 5-3 Double-Sideband Suppressed
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Sec. 5-4 Costas Loop and Squaring L
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Sec. 5-5 Asymmetric Sideband Signal
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Sec. 5-6 Phase Modulation and Frequ
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Sec. 5-7 Frequency-Division Multipl
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Sec. 5-8 FM Broadcast Technical Sta
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Sec. 5-9 Binary Modulated Bandpass
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( ( Sec. 5-9 Binary Modulated Bandp
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Sec. 5-10 Multilevel Modulated Band
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TABLE 5-7 Data V.32BIS AND V.33 MOD
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Sec. 5-11 Minimum-Shift Keying and
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Sec. 5-12 Orthogonal Frequency Divi
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Sec. 5-12 Orthogonal Frequency Divi
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Sec. 5-13 Spread Spectrum Systems 3
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Sec. 5-15 Study-Aid Examples 397 so
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Sec. 5-15 Study-Aid Examples 399 SA
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PROBLEMS Problems 401 ★ 5-1 An AM
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Problems 403 v 3 (t) Low-pass filte
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Problems 405 5-25 A transmitter pro
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Problems 407 5-41 A frequency modul
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Problems 409 FM receiver FM detecto
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Problems 411 (d) Sketch the wavefor
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Problems 413 (a) Show that the Gaus
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Sec. 6-1 Some Basic Definitions 415
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Sec. 6-2 Power Spectral Density 425
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` Sec. 6-2 Power Spectral Density 4
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Sec. 6-3 DC and RMS Values for Ergo
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Sec. 6-4 Linear Systems 439 Example
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Sec. 6-4 Linear Systems 441 x (t) h
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Sec. 6-4 Linear Systems 443 Example
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Sec. 6-5 Bandwidth Measures 445 The
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Sec. 6-6 The Gaussian Random Proces
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Sec. 6-6 The Gaussian Random Proces
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Sec. 6-7 Bandpass Processes 451 or,
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Sec. 6-7 Bandpass Processes 453 cer
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Sec. 6-7 Bandpass Processes 455 p v
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Sec. 6-7 Bandpass Processes 457 12.
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Sec. 6-7 Bandpass Processes 459 Pro
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Sec. 6-7 Bandpass Processes 461 Thu
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Sec. 6-7 Bandpass Processes 463 f R
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` ` Sec. 6-8 Matched Filters 465 Pr
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Sec. 6-8 Matched Filters 467 Equati
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Sec. 6-8 Matched Filters 469 occur
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Sec. 6-8 Matched Filters 471 so whi
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Sec. 6-8 Matched Filters 473 r(t)=s
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Sec. 6-9 Summary 475 6-9 SUMMARY A
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` ` ` Sec. 6-10 Appendix: Proof of
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` Sec. 6-11 Study-Aid Examples 479
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Problems 481 SA6-4 PSD for a Bandpa
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Problems 483 The power of n 1 (t) i
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Problems 485 1 2 x (f) = e N 0, ƒ
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Problems 487 6-42 A bandpass WSS ra
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Problems 489 6-54 A narrowband-sign
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Problems 491 6-60 Let be a wideband
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Sec. 7-1 Error Probabilities for Bi
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Sec. 7-2 Performance of Baseband Bi
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Sec. 7-3 Coherent Detection of Band
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Sec. 7-4 Noncoherent Detection of B
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Sec. 7-5 Quadrature Phase-Shift Key
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Sec. 7-6 Comparison of Digital Sign
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Sec. 7-6 Comparison of Digital Sign
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Sec. 7-7 Output Signal-to-Noise Rat
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TABLE 7-2 COMPARISON OF ANALOG SIGN
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Sec. 7-11 Study-Aid Examples 553 1.
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Sec. 7-11 Study-Aid Examples 555 1.
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Sec. 7-11 Study-Aid Examples 557 by
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Sec. 7-11 Study-Aid Examples 559 (d
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Problems 561 7-5 A whole binary com
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Problems 563 (a) Draw a block diagr
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Problems 565 where u c is the start
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Problems 567 (c) Plot (S/N) out vs.
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C h a p t e r WIRE AND WIRELESS COM
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Sec. 8-2 Telephone Systems 571 Tele
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Sec. 8-2 Telephone Systems 573 The
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Sec. 8-2 Telephone Systems 575 Subs
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Sec. 8-3 Digital Subscriber Lines (
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Sec. 8-5 Satellite Communication Sy
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585 Microwave relay Communication s
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Sec. 8-6 Link Budget Analysis 597 t
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Sec. 8-6 Link Budget Analysis 599 T
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ƒ ƒ Sec. 8-6 Link Budget Analysis
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ƒ ƒ Sec. 8-6 Link Budget Analysis
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Sec. 8-6 Link Budget Analysis 605 o
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Sec. 8-6 Link Budget Analysis 607 o
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Sec. 8-6 Link Budget Analysis 609 w
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Sec. 8-6 Link Budget Analysis 611 U
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Sec. 8-6 Link Budget Analysis 613 E
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Sec. 8-6 Link Budget Analysis 615 2
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Sec. 8-6 Link Budget Analysis 617 F
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Sec. 8-7 Fiber-Optic Systems 619 fi
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Sec. 8-8 Cellular Telephone Systems
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TABLE 8-10 1G MAJOR ANALOG FDMA CEL
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TABLE 8-11 2G MAJOR DIGITAL CELLULA
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Sec. 8-9 Television 631 Camera Targ
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Sec. 8-9 Television 633 The composi
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Sec. 8-9 Television 635 Composite b
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Sec. 8-9 Television 637 pulses. The
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Sec. 8-9 Television 639 from the qu
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Sec. 8-9 Television 641 the x-axis
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Sec. 8-9 Television 643 1 Max. carr
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TABLE 8-13 U.S. TELEVISION AND CABL
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647 52 PP 698.00 - 704.00 390.00 -
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Sec. 8-9 Television 649 encryption
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Sec. 8-9 Television 651 Fig. 5-33,
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Sec. 8-10 Cable Data Modems 653 •
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Sec. 8-11 Wireless Data Networks 65
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Sec. 8-13 Study-Aid Examples 657 TA
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Sec. 8-13 Study-Aid Examples 659 Th
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Sec. 8-13 Study-Aid Examples 661 ca
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Problems 663 8-10 A digital TV stat
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Problems 665 ★ 8-26 A TV set is c
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Problems 667 the IF band of the sat
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A p p e n d i x MATHEMATICAL TECHNI
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A-4 Integral Calculus 671 d sin ax
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A-5 Integral Tables 673 L x2 cos x
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A-8 The Dirac Delta Function 675 A-
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A-9 Tabulation of Sa(x) = (sin x)/x
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A-10 Tabulation of Q (z) 679 z Q(z)
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B-2 Sets 681 used when conversing w
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B-3 Probability and Relative Freque
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B-5 Cumulative Distribution Functio
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B-6 Ensemble Average and Moments 69
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B-7 Examples of Important Distribut
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B-8 Functional Transformations of R
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B-8 Functional Transformations of R
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B-9 Multivariate Statistics 709 B-9
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B-9 Multivariate Statistics 711 Pro
Page 1474: B-9 Multivariate Statistics 713 x 1
Page 1478: B-9 Multivariate Statistics 715 Cen
Page 1482: Problems 717 ★ B-4 A die is tosse
Page 1486: Problems 719 B-20 Let x be a random
Page 1490: Problems 721 (a) Verify that f(x 1
Page 1494: A p p e n d i x USING MATLAB MATLAB
Page 1498: C-3 Programming in MATLAB 725 4. At
Page 1502: REFERENCES ABRAMOWITZ, M., and I. A
Page 1506: References 729 BÖRJESSON P. O., an
Page 1510: References 731 FIKE, J. L., and G.
Page 1514: References 733 JENKINS, M. G., and
Page 1518: References 735 NYQUIST, H., “Cert
Page 1522: References 737 SHANMUGAN, K. S., Di
Page 1528: 740 Answers to Selected Problems Ch
Page 1532: 742 Answers to Selected Problems 2
Page 1536: 744 Answers to Selected Problems 5-
Page 1540: 746 Answers to Selected Problems h
Page 1544: 748 Index Amplitude shift keying (A
Page 1548: 750 Index Coding/codes (cont.) chan
Page 1552: 752 Index Effective isotropic radia
Page 1556: 754 Index In-phase components, 638
Page 1560: 756 Index Multilevel signaling, 157
Page 1564: 758 Index Process/processing (cont.
Page 1568: 760 Index Signal/signaling (cont.)
Page 1572: 762 Index Two-level data, 165 Two-q
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TABLE 2-2 SOME FOURIER TRANSFORM PA
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