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Question 4-) Let Fourier Transform of the signal r(t) be X(jw). Assume that g(t) satisfies the equation g(t) = X(jt). (a) Show that the Fourier transform G(jw) of g(t) has the shape of 2x(−t), that is G(jw) = 2nx(-w). (b) Using the fact that F{d(t + ß)} F{eißt} = 2nd(w – ß). ew with the result from part a, show that

Question 4-) Let Fourier Transform of the signal r(t) be X(jw). Assume that g(t) satisfies the equation g(t) = X(jt). (a) Show that the Fourier transform G(jw) of g(t) has the shape of 2x(−t), that is G(jw) = 2nx(-w). (b) Using the fact that F{d(t + ß)} F{eißt} = 2nd(w – ß). ew with the result from part a, show that

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question 4-) Let Fourier Transform of the signal #(t) be X(jw). Assume that g(t) satisfies the equation g(t) = X(jt). (a) Show that the Fourier transform G(jw) of g(t) has the shape of 2nx(-t), that is G(jw) = 2rx(-w). (b) Using the fact that F{8(t+ B)} = e]$w with the result from part a, show that F{ej$t} = 2nd(w – B).
Transcribed Image Text:Question 4-) Let Fourier Transform of the signal #(t) be X(jw). Assume that g(t) satisfies the equation g(t) = X(jt). (a) Show that the Fourier transform G(jw) of g(t) has the shape of 2nx(-t), that is G(jw) = 2rx(-w). (b) Using the fact that F{8(t+ B)} = e]$w with the result from part a, show that F{ej$t} = 2nd(w – B).
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