GATE EE 2014 Set 1 — Question 45
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Signals & Systems → Fourier Analysis & Sampling → Fourier Transform Properties
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Question
Let be a continuous time signal and let be its Fourier Transform defined byDefine byWhat is the relationship between and ?
Correct answer
(B) g(t) would be proportional to f(t) if f(t) is an even function.
Solution
The inverse Fourier transform is defined as:
Replacing with :
Given . By changing the dummy variable to , we see:
For to be proportional to , we need . This is true if is an even function () or an odd function (). Option (B) provides a correct sufficient condition.
Replacing with :
Given . By changing the dummy variable to , we see:
For to be proportional to , we need . This is true if is an even function () or an odd function (). Option (B) provides a correct sufficient condition.
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