GATE EE 2018 Set 1 — Question 50
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Signals & Systems → Fourier Analysis & Sampling → CTFT & DTFT
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Question
The Fourier transform of a continuous-time signal is given bywhere and denotes frequency. Then the value of at is ___________ (up to 1 decimal place). ( denotes the logarithm to base )
Correct answer
9.5 to 10.5
Solution
Given the Fourier transform .
Using the standard Fourier transform pair , we identify .
Thus, the time-domain signal is .
At :
.
Taking the natural logarithm:
.
The absolute value is:
.
Using the standard Fourier transform pair , we identify .
Thus, the time-domain signal is .
At :
.
Taking the natural logarithm:
.
The absolute value is:
.
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