Consider the system where for an input x(t) the output is y(t) = x(t)f(t).

(a) Let f(t) = u(t) − u(t − 10), determine whether the system with input x(t) and output y(t) is linear, time-invariant, causal, and BIBO stable.

(b) Suppose x(t) = 4cos(π t/2), and f(t) = cos(6π t/7) and both are periodic, is the output y(t) also periodic? What frequencies are present in the output? Is this system linear? Is it time-invariant? Explain.

(c) Let f(t) = u(t) − u(t − 2) and the input x(t) = u(t), find the corresponding output y(t). Suppose you shift the input so that it is x₁(t) = x(t − 3) what is the corresponding output y₁(t)? Is the system time-invariant? Explain.