The input-output relationship of a system is

where x(t) is the input and y(t) the output.

(a) Let the input be x(t) = sin(2Ï€t) u(t), plot the corresponding output y(t). What is the output of the system if we double the input? That is, what is the output y₁(t) if the input x₁(t) = 2x(t) = 2 sin(2Ï€t) u(t)? Is the system linear or not?

(b) Is the given system time-invariant?

Transcribed Image Text:

if x(t) > 0 if x(t) < 0 y(t) = sign(x(t)) = -1