Question

For which of the following a Fourier series cannot be defined?

(a) 3 sin (25t)

(b) 4 cos (20t + 3) + 2 sin (710t)

(c) exp(-|t|) sin (25t)

(d) 1

This question was addressed to me in unit test.

Asked question is from Miscellaneous Examples on Fourier Series topic in section Fourier Series of Signals and Systems

Answer 1

Right choice is (c) exp(-|t|) sin (25t)

Easy explanation: 3 sin (25) = 25

4 cos (20  + 3) + 2sin (710) sum of two periodic function is also periodic function

For 1 which is a constant, Fourier series exists.

For exp (-|t|) sin (25t), due to decaying exponential decaying function, it is not periodic. So Fourier series cannot be defined for it.