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) = -6(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.
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) = -6(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.
Introductory Circuit Analysis (13th Edition)
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Publisher:Robert L. Boylestad
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![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)].](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6128a30d-be3c-4f5f-a17a-54eaa3ca9284%2Fefb3ddf6-e5e9-4a83-a616-676000432f62%2Fg5h2o1_processed.png&w=3840&q=75)
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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