Question

If x(t) and y(t) are two periodic signals with coefficients Xn and Yn then the linearity is represented as?

(a) ax(t) + by(t) = aXn + bYn

(b) ax (t) + by(t) = Xn + bYn

(c) ax(t) + by(t) = aXn + Yn

(d) ax(t) + by(t) = Xn + Yn

The question was posed to me in examination.

The origin of the question is Fourier Series Properties in section Fourier Series of Signals and Systems

Answer 1

Right answer is (a) ax(t) + by(t) = aXn + bYn

Easiest explanation: ax(t) + by(t) = aXn + bYn,  x(t) and y(t) are two periodic signals with coefficients Xn and Yn.