A periodic signal x(t) has a trigonometric Fourier series expansion x (t) = a_{0} + \sum ↙\stackrel{\infty}{n = 1}⁡(a_{n}\:\cos\:n\:\omega _{0}t + b_{n} \sin ⁡n\:\omega _{0}t) If x(t) = -x (- t) = -x (t - π/ω 0 ), we can conclude that

Correct Answer is : an are zero for all n and bn are zero for n even

a n are zero for all n and b n are zero for n even

a n are zero for all n and b n are zero for n odd

a n are zero for n even and b n are zero for n odd

a n are zero for n odd and b n are zero for n even

GATE Electronics and Communications (EC) 2017 Shift 1 Solved Paper

Question : 18 of 65

Marks: +1, -0

A periodic signal x(t) has a trigonometric Fourier series expansion

x (t) = a_{0} + ∑ ↙{n = 1}↖{∞}⁡(a_{n}\:cos\:n\:ω _{0}t + b_{n} sin \;⁡n\:ω _{0}t)

If x(t) = -x (- t) = -x (t - π/ω₀), we can conclude that

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