GATE EC 2015 Set 3 — Question 54
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Signals & Systems → Discrete-Time Signals → DFT & FFT
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Question
Let be a periodic signal with period 16. Its DFS coefficients are defined by for all . The value of the coefficient is ______.
Correct answer
0.48 to 0.52
Solution
The signal is . Using Euler's identity:
The DFS coefficients for a period represent the signal as .
Comparing the terms:
.
Since , we have .
The DFS coefficients for a period represent the signal as .
Comparing the terms:
.
Since , we have .
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