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GATE EC 2018 Set 1 — Question 24

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MCQ+1 / -0.33MediumFourier SeriesContinuous-Time SignalsSignals & Systems

Signals & Systems → Continuous-Time Signals → Fourier Series

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Let x(t)x(t) be a periodic function with period T=10T = 10. The Fourier series coefficients for this series are denoted by aka_k, that isx(t)=∑k=−∞∞akejk2πTtx(t) = \sum_{k=-\infty}^{\infty} a_k e^{j k \frac{2\pi}{T} t}The same function x(t)x(t) can also be considered as a periodic function with period T′=40T' = 40. Let bkb_k be the Fourier series coefficients when period is taken as T′T'. If ∑k=−∞∞∣ak∣=16\sum_{k=-\infty}^{\infty} |a_k| = 16, then ∑k=−∞∞∣bk∣\sum_{k=-\infty}^{\infty} |b_k| is equal to
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