Let 𝑥(𝑡) be a periodic function with period 𝑇 = 10. The Fourier series coefficients for this series are denoted by 𝑎 𝑘 , that is $$x\left( t \right) = \sum\limits_{k = - \infty }^\infty {{a_k}} {e^{jk{{2\pi } \over T}t}}$$ The same function 𝑥(𝑡) can also be considered as a periodic function with period T' = 40. Let b k be the Fourier series coefficients when period is taken as T'. If $$\sum\limits_{k = - \infty }^\infty {\left| {{a_k}} \right|} = 16$$, then $$\sum\limits_{k = - \infty }^\infty {\left| {{b_k}} \right|} = 16$$ is equal to

GATE 2018 Electronics & Communication PYQ — Signals and Systems

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Signals and Systems · Fourier Series

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Recurring concept

Fourier Series has appeared in GATE Electronics & Communication 15 times across 12 years (2017, 2018, 2021, 2023, 2025, ...).