Question

The Fourier series coefficient of the signal y(t) = x(4t-1) is ______________

(a) \(\frac{8π}{T} X[k]\)

(b) \(\frac{4π}{T}X[k]\)

(c) \(e^{-jk \frac{8π}{T}} X[k]\)

(d) \(e^{jk \frac{8π}{T}} X[k]\)

This question was addressed to me in unit test.

I'd like to ask this question from Fourier Series Coefficients topic in portion Fourier Series of Signals and Systems

Answer 1

The correct choice is (c) \(e^{-jk \frac{8π}{T}} X[k]\)

Easiest explanation: The period of x (4t) is a fourth of the period of x (t). The Fourier series coefficient of x (4t) is still X[k]. Hence, the coefficient of x (4t-1) is \(e^{-jk \frac{8π}{T}} X[k]\).