Note that you may need to use the geometric progression equations in the following ques- tions. 1-Find the Fourier-transform (FT), for the following signals: - (a) x1(n) = −8(n + 2) + d(n − 2). As this is an odd function, show that the FT is a pure imaginary function of frequency. (b) x2(n) = -8(n) + (n-2). Calculate it in two ways, first directly, and second by relating it to the signal in the previous part, and then using the properties of the Fourier transform. (c) x3(n) = d(n+2)+58(n) + d(n − 2). As this is an even function, show that the FT is a real function of frequency. (d) vi(n) = (-0.9)”−¹u(n − 1), (e) v2(n) = (-0.9)u(n − 1), (f) h(n) = 2[u(n) – u(n − 80)]. 2- If then show that ∞ x(n)X(jw) Σx(n) = lim X(ew). n=-∞ 04-3 Verify this relationship by using the results in parts (b), (c), (d), and (f), in problem 1. sin(Kw) (In part (f), you may use the fact that limw→0 sin(0.5w) 2K.)

Note that you may need to use the geometric progression equations in the following ques- tions. 1-Find the Fourier-transform (FT), for the following signals: - (a) x1(n) = −8(n + 2) + d(n − 2). As this is an odd function, show that the FT is a pure imaginary function of frequency. (b) x2(n) = -8(n) + (n-2). Calculate it in two ways, first directly, and second by relating it to the signal in the previous part, and then using the properties of the Fourier transform. (c) x3(n) = d(n+2)+58(n) + d(n − 2). As this is an even function, show that the FT is a real function of frequency. (d) vi(n) = (-0.9)”−¹u(n − 1), (e) v2(n) = (-0.9)u(n − 1), (f) h(n) = 2[u(n) – u(n − 80)]. 2- If then show that ∞ x(n)X(jw) Σx(n) = lim X(ew). n=-∞ 04-3 Verify this relationship by using the results in parts (b), (c), (d), and (f), in problem 1. sin(Kw) (In part (f), you may use the fact that limw→0 sin(0.5w) 2K.)

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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