Consider the pulse x(t) = u(t) u(t 1). Find the zeros and poles of X(s)and plot them. (a) Suppose x(t)is the input of a LTI

Consider the pulse x(t) = u(t) ˆ’ u(t ˆ’ 1). Find the zeros and poles of X(s)and plot them.

(a) Suppose x(t)is the input of a LTI system with a transfer function H(s) = Y(s)/X(s) = 1/(s² + 4Ï€²), find and plot the poles and zeros of Y(s) = L[y(t)]), where y(t)is the output of the system.

(b) If the transfer function of the LTI system is

and the input is the above signal x(t), compute the output z(t).

Z(s) X(s) -!? G(s) .2 + (2kл)? k=1