Question

The system characterized by the equation y (t) = ax (t) + b is ____________

(a) Linear for any value of b

(b) Linear if b>0

(c) Linear if b<0

(d) Non-linear

This question was addressed to me by my school teacher while I was bunking the class.

The doubt is from Average Power and Energy of a Signal topic in section Fourier Series of Signals and Systems

Answer 1

Right choice is (d) Non-linear

The explanation is: The system is non-linear. The principle of homogeneity states that if for any input signal X (t), i.e. scaling any input signal scales the output signal by the same factor, then the signal X (t) is homogeneous. Because x (t) does not lead to y (t) = 0, which is a direct violation of the principle of homogeneity.