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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(22) + jsin(20) (b) X(e)= sin() + cos(). [1, π/4 < | < 3π/4, otherwise (c) |X(en) = {1; 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).

3.53 Use the equation describing the DTFT representa- tion to determine the time-domain signals corre- sponding to the following DTFTS: (a) X(e) cos(22) + jsin(20) (b) X(e)= sin() + cos(). [1, π/4 < | < 3π/4, otherwise (c) |X(en) = {1; 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).

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
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Can you please solve 3.53 b and d step by step original solution

E Q 3.53 Use the equation describing the DTFT representa- tion to determine the time-domain signals corre- sponding to the following DTFTs: (a) X(en) = cos(20) + sin(20) (b) X(en) = sin() + cos(/). (c) X(en) 1, π/4 < | <3π/4, 0, otherwise arg{X(e)} = -4 (d) X(e) as depicted in Figure P3.53(a). (e) X(en) 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)=-oa"(tm), a < 1 (e) x(t) as depicted in Figure P3.54(a). (f) x(t) as depicted in Figure P3.54(b). 342 3.55 Use the equation describing the FT representation to determine the time-domain signals corresponding to the following FTs: (a) X(jw) = (cos(2w), w < 0, otherwise of 820 -2T -2T -2πT X(e) tr -2π -T (a) IX(e)| sin (12) M.M.M. 0 arg{X(e)} 2π + J. 0 म <-T -2п (b) IX(e)| -TT-TT/21 TT/2 0 TT arg{X(e)} T 2π T 2T 3T 2T +8 3π 1
Transcribed Image Text:E Q 3.53 Use the equation describing the DTFT representa- tion to determine the time-domain signals corre- sponding to the following DTFTs: (a) X(en) = cos(20) + sin(20) (b) X(en) = sin() + cos(/). (c) X(en) 1, π/4 < | <3π/4, 0, otherwise arg{X(e)} = -4 (d) X(e) as depicted in Figure P3.53(a). (e) X(en) 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)=-oa"(tm), a < 1 (e) x(t) as depicted in Figure P3.54(a). (f) x(t) as depicted in Figure P3.54(b). 342 3.55 Use the equation describing the FT representation to determine the time-domain signals corresponding to the following FTs: (a) X(jw) = (cos(2w), w < 0, otherwise of 820 -2T -2T -2πT X(e) tr -2π -T (a) IX(e)| sin (12) M.M.M. 0 arg{X(e)} 2π + J. 0 म <-T -2п (b) IX(e)| -TT-TT/21 TT/2 0 TT arg{X(e)} T 2π T 2T 3T 2T +8 3π 1
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