Consider an averager represented by the input/output equation where x(t) is the input and y(t) the output.
Question:
where x(t) is the input and y(t) the output.
(a) Let the input be x1(t) = δ(t), find graphically the corresponding output y1(t) for ˆ’ˆž < t < ˆž. Let then the input be x2(t) = 2x1(t), find graphically the corresponding output y2(t) for ˆ’ˆž < t < ˆž. Is y2(t) = 2y1(t)? Is the system linear?
(b) Suppose the input is x3(t) = u(t) ˆ’ u(t ˆ’ 1), graphically compute the corresponding output y3(t) for ˆ’ˆž < t < ˆž. If a new input is x4(t) = x3(t ˆ’ 1) = u(t ˆ’ 1) ˆ’ u(t ˆ’ 2), find graphically the corresponding output y4(t) for ˆ’ˆž < t < ˆž, and indicate if y4(t) = y3(t ˆ’ 1). Accordingly, would this averager be time-invariant?
(c) Is this averager a causal system? Explain.
(d) If the input to the averager is bounded, would its output be bounded? Is the averager BIBO stable?
Step by Step Answer:
a Input x 1 t t gives x 2 t 2x 1 t gives Since y 2 t 2yt system is nonlinear Figure ...View the full answer
