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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) +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) = 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) v₁(n) = (-0.9)”−¹u(n − 1), (e) v2(n) = (-0.9)u(n − 1), (f) h(n) = 2[u(n) – u(n − 80)]. -

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) +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) = 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) v₁(n) = (-0.9)”−¹u(n − 1), (e) v2(n) = (-0.9)u(n − 1), (f) h(n) = 2[u(n) – u(n − 80)]. -

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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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) +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) = 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) v₁(n) = (-0.9)”−¹u(n − 1), (e) v2(n) = (-0.9)u(n − 1), (f) h(n) = 2[u(n) – u(n − 80)]. -
Transcribed Image Text: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) +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) = 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) v₁(n) = (-0.9)”−¹u(n − 1), (e) v2(n) = (-0.9)u(n − 1), (f) h(n) = 2[u(n) – u(n − 80)]. -
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