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-2 -1 1 0 (a) FIGURE P3.54 子

-2 -1 1 0 (a) FIGURE P3.54 子

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
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Please solve 3.54 (e) step by step original solution

326 (e) X(jw) as depicted in Figure P3.55(b). (f) X(jw) as depicted in Figure P3.55(c). -2 x(1) -1 1 0 (a) FIGURE P3.54 2 -2 t IX(jw)| 1 0 arg{X(jw)) CHAPTER 3 FOURIER REPRESENTATIONS OF SIGNALS AND LINEAR TIME-INVARIANT SYSTEMS 2 2 x(t) 0 (b) 343 2 of 820 FIGURE P3.53 (c) 3.56 Determine the appropriate Fourier representations of the following time-domain signals, using the defin- ing equations: (a) x(t) = ecos(2πt)u(t) (b) x[n] = (cos(ion) + jsin(n), |-|< 10 0, otherwise (c) x[n] as depicted in Figure P3.56(a). (d) x(t) = e¹tu(-t + 2) (e) x(t) = sin(2πt)| (f) x[n] as depicted in Figure P3.56(b). (g) x(t) as depicted in Figure P3.56(c). 3.57 Determine the time-domain signal corresponding to each of the following frequency-domain representa- tions: (a) X[k]: = e-kw/2, k < 10 0, otherwise Fundamental period of time domain signal is T = 1. 7 K
Transcribed Image Text:326 (e) X(jw) as depicted in Figure P3.55(b). (f) X(jw) as depicted in Figure P3.55(c). -2 x(1) -1 1 0 (a) FIGURE P3.54 2 -2 t IX(jw)| 1 0 arg{X(jw)) CHAPTER 3 FOURIER REPRESENTATIONS OF SIGNALS AND LINEAR TIME-INVARIANT SYSTEMS 2 2 x(t) 0 (b) 343 2 of 820 FIGURE P3.53 (c) 3.56 Determine the appropriate Fourier representations of the following time-domain signals, using the defin- ing equations: (a) x(t) = ecos(2πt)u(t) (b) x[n] = (cos(ion) + jsin(n), |-|< 10 0, otherwise (c) x[n] as depicted in Figure P3.56(a). (d) x(t) = e¹tu(-t + 2) (e) x(t) = sin(2πt)| (f) x[n] as depicted in Figure P3.56(b). (g) x(t) as depicted in Figure P3.56(c). 3.57 Determine the time-domain signal corresponding to each of the following frequency-domain representa- tions: (a) X[k]: = e-kw/2, k < 10 0, otherwise Fundamental period of time domain signal is T = 1. 7 K
FIGURE P3.52 3.53 Use the equation describing the DTFT representa- tion to determine the time-domain signals corre- sponding to the following DTFTs: (a) X(e) = cos(20) +isin(20) (b) X(e) = sin(n) + cos(). (c) |X(e) = [1, π/4 < | < 3π/4, otherwise arg{X(e)}: = -40 (d) X(e) as depicted in Figure P3.53(a). (e) X(e) as depicted in Figure P3.53(b). (f) X(e) as depicted in Figure P3.53(c). 3.54 Use the defining equation for the FT to evaluate the frequency-domain representations of the following signals: (a) x(t) = eu(t - 3) (b) x(t) = e (c) x(t) = te 'u(t) (d) x(t) = m-am8(tm), al < 1 (e) x(t) as depicted in Figure P3.54(a). (f) x(t) as depicted in Figure P3.54(b). 3.55 Use the equation describing the FT representation to determine the time-domain signals corresponding to the following FTs: (a) X(jw) = (b) X(jw) eu (w) = (c) X(jw) = elad (d) X(jw) as depicted in Figure P3.55(a). (e) X(jw) as depicted in Figure P3.55(b). (f) X(jw) as depicted in Figure P3.55(c). (cos(2w), w < 0, otherwise Y -2π ... -2π -2π -2π X(e) FIGURE P3.53 IX(e)| MMM.. m/2 -T-TT/2 0 (a) 0 arg(X(e)} 2π- 未 -T 0 -2π -#-#12 sin (52) (b) IX(e)| 1 -"/2 -TT 0 arg{X(e)) 0 T TT/2 TT/2 म (c) 2π т 2π fi 2π 3π +9 3π 2π 2T Q Ω
Transcribed Image Text:FIGURE P3.52 3.53 Use the equation describing the DTFT representa- tion to determine the time-domain signals corre- sponding to the following DTFTs: (a) X(e) = cos(20) +isin(20) (b) X(e) = sin(n) + cos(). (c) |X(e) = [1, π/4 < | < 3π/4, otherwise arg{X(e)}: = -40 (d) X(e) as depicted in Figure P3.53(a). (e) X(e) as depicted in Figure P3.53(b). (f) X(e) as depicted in Figure P3.53(c). 3.54 Use the defining equation for the FT to evaluate the frequency-domain representations of the following signals: (a) x(t) = eu(t - 3) (b) x(t) = e (c) x(t) = te 'u(t) (d) x(t) = m-am8(tm), al < 1 (e) x(t) as depicted in Figure P3.54(a). (f) x(t) as depicted in Figure P3.54(b). 3.55 Use the equation describing the FT representation to determine the time-domain signals corresponding to the following FTs: (a) X(jw) = (b) X(jw) eu (w) = (c) X(jw) = elad (d) X(jw) as depicted in Figure P3.55(a). (e) X(jw) as depicted in Figure P3.55(b). (f) X(jw) as depicted in Figure P3.55(c). (cos(2w), w < 0, otherwise Y -2π ... -2π -2π -2π X(e) FIGURE P3.53 IX(e)| MMM.. m/2 -T-TT/2 0 (a) 0 arg(X(e)} 2π- 未 -T 0 -2π -#-#12 sin (52) (b) IX(e)| 1 -"/2 -TT 0 arg{X(e)) 0 T TT/2 TT/2 म (c) 2π т 2π fi 2π 3π +9 3π 2π 2T Q Ω
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