The input-output equation characterizing an amplifier that saturates once the input reaches certain values is

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

(a) Plot the relation between the input x(t) and the output y(t). Is this a linear system? For what range of input values is the system linear, if any?

(b) Suppose the input is a sinusoid x(t) = 20 cos(2Ï€t) u(t), carefully plot x(t) and y(t) for t = ˆ’2 to 4.

(c) Let the input be delayed by 2 units of time, i.e, the input is x₁(t) = x(t ˆ’ 2) find the corresponding output y₁(t), and indicate how it relates to the output y(t) due to x(t) found above. Is the system time-invariant?

Transcribed Image Text:

100x(t) - 10 < x(t) < 10 x(t) > 10 x(t) < - 10 y(t) = 1000 - 1000