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(b) x2(n) = -8(n)+8(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) = 8(n + 1) + 5 + 8(n – 1). As this is an even function, show that the FT is a real

(b) x2(n) = -8(n)+8(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) = 8(n + 1) + 5 + 8(n – 1). As this is an even function, show that the FT is a real

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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answer part b,please.

x(n) + X(e) then show that E x(n) = lim X(ej«). n=-0 Verify this relationship by using the results in parts (b), (c), (d), and (f), in problem 1. (In part (f), you may use the fact that lim0 sin(Kw) sin(0.5w) - 2K.)
Transcribed Image Text:x(n) + X(e) then show that E x(n) = lim X(ej«). n=-0 Verify this relationship by using the results in parts (b), (c), (d), and (f), in problem 1. (In part (f), you may use the fact that lim0 sin(Kw) sin(0.5w) - 2K.)
1-Find the Fourier-transform (FT), for the following signals: (a) x1(n) = -8(n + 1) + 8(n –- 1). As this is an odd function, show that the FT is a pure imaginary function of frequency. (b) x2(n) = -8(n)+8(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) = 8(n + 1) + 5 + 8(n – 1). As this is an even function, show that the FT is a real function of frequency. (d) vi(n) = (–0.9)"-lu(n – 1), (e) v2(n) = (-0.9)"u(n – 1), (f) h(n) = 2[u(n) – u(n – 80)].
Transcribed Image Text:1-Find the Fourier-transform (FT), for the following signals: (a) x1(n) = -8(n + 1) + 8(n –- 1). As this is an odd function, show that the FT is a pure imaginary function of frequency. (b) x2(n) = -8(n)+8(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) = 8(n + 1) + 5 + 8(n – 1). As this is an even function, show that the FT is a real function of frequency. (d) vi(n) = (–0.9)"-lu(n – 1), (e) v2(n) = (-0.9)"u(n – 1), (f) h(n) = 2[u(n) – u(n – 80)].
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