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GATE EC 2021 Set 1 — Question 49

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NAT+2 / -0MediumFourier SeriesContinuous-Time SignalsSignals & SystemsParseval's Theorem

Signals & Systems → Continuous-Time Signals → Fourier Series

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The exponential Fourier series representation of a continuous-time periodic signal x(t)x(t) is defined asx(t)=∑k=−∞∞akejkω0tx(t) = \sum_{k=-\infty}^{\infty} a_k e^{j k \omega_0 t}where ω0\omega_0 is the fundamental angular frequency of x(t)x(t) and the coefficients of the series are aka_k. The following information is given about x(t)x(t) and aka_k.
I. x(t)x(t) is real and even, having a fundamental period of 6
II. The average value of x(t)x(t) is 2
III. ak={k,1≤k≤30,k>3a_k = \begin{cases} k, & 1 \leq k \leq 3 \\ 0, & k > 3 \end{cases}The average power of the signal x(t)x(t) (rounded off to one decimal place) is ________.
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