A sinc signal x(t) = sin(0.5t)/(t)is passed through an ideal low-pass filter with a frequency response H(j)

A sinc signal x(t) = sin(0.5t)/(πt)is passed through an ideal low-pass filter with a frequency response H(jΩ) = u(Ω + 0.5) − u(Ω − 0.5)

(a) Find the Fourier transform X(Ω)and carefully plot it.

(b) Find the output y(t) of the filter by calculating first Y(Ω). What is the convolution integral of x(t) with x(t)? Explain.