The input to an LTI system such as Fig. 1. is defined by the equation(a) Determine the Fou...

The input to an LTI system such as Fig. 1. is defined by the equation

(a) Determine the Fourier transform of x(t) and plot it on a graph that spans the frequency range – 1000π ≤ ω ≤ 1000π

(b) Suppose that the frequency response of the LTI system is given by the following equation:

Plot this function on the graph that you constructed in part (a).

(c) Determine the DC value of the output signal; i.e.,

Determine  where T0 is the period of the output signal.

(d) Write an equation for y(t). If possible, simplify it to include only cosine functions