2.7 Consider the system where for an input x(†) 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 (1) and output y(t) is linear,...

Extracted text: 2.7 Consider the system where for an input x(†) 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 (1) and output y(t) is linear, time-invariant, causal and BIBO stable. (b) Suppose x (t) = 4 cos(nt/2), and f(t) = cos(6A1/7) 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 (1), find the corresponding output y(t). Suppose you shift the input so that it is x1(t) = r(t – 3); what is the corresponding output yı (1)? Is the system time-invariant? Explain. Answer: (a) System is time-varyîng, BIBO stable.