The following sampling system will be used for the next few problems. An input signal r(t) is passed 2 through an anti-aliasing filter Ha (w) before it is sampled at T = seconds. The resulting sampled signal 5 2 xg(t) is then passed through a reconstruction filter with frequency spectrum H,(w) = rect (5). 5 x(t) Anti-Aliasing Filter: Ha(w) Ta(t) sampler: ST, (t) x, (t) Reconstruction Filter: H, (w) r(t) = sinc xr(t) Problem 6 Determine and sketch the CTFT of anti-aliasing filter Ha(w) -12 w 12 with maximum cutoff frequency to prevent aliasing. Hint: It should have magnitude equal to one and a cutoff frequency in rad/sec we wg /2 (half the Nyquist rate). = Problem 7 We now want to take the same signal of an anti-aliasing filter you designed in Problem 6. (a) Determine and sketch X(w) for -12