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Problem 1 (3 pts each). Using the definition, find the Fourier transform of the signal in textbook problem 4.21(a), page 338. Then, for a = 0.5 and w₁ = 2, evaluate the magnitude and the phase angle of the Fourier spectrum X(jw) at: (a) w = 0; (Q1, Q2) (b) w = 1; (Q3, Q4) (c) w = 2; (Q5, Q6) (d) w = 4; (Q7, Q8) 4.21. Compute the Fourier transform of each of the following signals: (a) [eat cos wot]u(t), a > 0 (c) x(t) = { ŏ 1+ cos πt, || ≤ 1 0, (e) [te sin 4t]u(t) |t| > 1 (g) x(t) as shown in Figure P4.21(a) (i) x(t) = { } 1-2, 0

Problem 1 (3 pts each). Using the definition, find the Fourier transform of the signal in textbook problem 4.21(a), page 338. Then, for a = 0.5 and w₁ = 2, evaluate the magnitude and the phase angle of the Fourier spectrum X(jw) at: (a) w = 0; (Q1, Q2) (b) w = 1; (Q3, Q4) (c) w = 2; (Q5, Q6) (d) w = 4; (Q7, Q8) 4.21. Compute the Fourier transform of each of the following signals: (a) [eat cos wot]u(t), a > 0 (c) x(t) = { ŏ 1+ cos πt, || ≤ 1 0, (e) [te sin 4t]u(t) |t| > 1 (g) x(t) as shown in Figure P4.21(a) (i) x(t) = { } 1-2, 0

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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Problem 1 (3 pts each). Using the definition, find the Fourier transform of the signal in textbook problem 4.21(a), page 338. Then, for a = 0.5 and w₁ = 2, evaluate the magnitude and the phase angle of the Fourier spectrum X(jw) at: (a) w = 0; (Q1, Q2) (b) w = 1; (Q3, Q4) (c) w = 2; (Q5, Q6) (d) w = 4; (Q7, Q8)
Transcribed Image Text:Problem 1 (3 pts each). Using the definition, find the Fourier transform of the signal in textbook problem 4.21(a), page 338. Then, for a = 0.5 and w₁ = 2, evaluate the magnitude and the phase angle of the Fourier spectrum X(jw) at: (a) w = 0; (Q1, Q2) (b) w = 1; (Q3, Q4) (c) w = 2; (Q5, Q6) (d) w = 4; (Q7, Q8)
4.21. Compute the Fourier transform of each of the following signals: (a) [eat cos wot]u(t), a > 0 (c) x(t) = { ŏ 1+ cos πt, || ≤ 1 0, (e) [te sin 4t]u(t) |t| > 1 (g) x(t) as shown in Figure P4.21(a) (i) x(t) = { } 1-2, 0<t<1 0, otherwise (b) e-3 sin 2t (d) oak 8(t-kT), |a| < 1 t (f) Sinsin 2(-1) πι π(1-1) (h) x(t) as shown in Figure P4.21(b) (j)Σ- e-t-2n x (t) x (t) (a) -6-5-4-3-2-10 1 2 (b) 3 4 5 6 7 8 t
Transcribed Image Text:4.21. Compute the Fourier transform of each of the following signals: (a) [eat cos wot]u(t), a > 0 (c) x(t) = { ŏ 1+ cos πt, || ≤ 1 0, (e) [te sin 4t]u(t) |t| > 1 (g) x(t) as shown in Figure P4.21(a) (i) x(t) = { } 1-2, 0<t<1 0, otherwise (b) e-3 sin 2t (d) oak 8(t-kT), |a| < 1 t (f) Sinsin 2(-1) πι π(1-1) (h) x(t) as shown in Figure P4.21(b) (j)Σ- e-t-2n x (t) x (t) (a) -6-5-4-3-2-10 1 2 (b) 3 4 5 6 7 8 t
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