GATE EE 2022 Set 1 — Question 49
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Signals & Systems → Fourier Analysis & Sampling → Fourier Series (CT & DT)
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Question
The discrete time Fourier series representation of a signal with period is written as . A discrete time periodic signal with period , has the non-zero Fourier series coefficients: and . The signal is
Correct answer
(B) 1 + 2e^((j(2π)/(6)n))cos((2π)/(6)n)
Solution
The DTFS coefficients of a signal with period are themselves periodic in with period 3, soand the remaining coefficient of one period is zero, . HenceNow simplify option (B) using with :which is exactly .The other choices reduce to different signals:
- (A):
- (C):
- (D):
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