Consider the sequence x[n] = 2δ[n] + δ[n − 1] − δ[n − 2]. (a) Determine the DTFT X(...

Consider the sequence x[n] = 2δ[n] + δ[n − 1] − δ[n − 2].

(a) Determine the DTFT X(e^jω) of x[n] and the DTFT Y(e^jω) of the sequence y[n] = x[−n].

(b) Using your results from part (a) find an expression for

(c) Using the result of part (b) make a plot of w[n] = x[n] ∗ y[n].

(d) Now plot the sequence y_p[n] = x[((−n))4] as a function of n for 0 ≤ n ≤ 3.

(e) Now use any convenient method to evaluate the four-point circular convolution of x[n] with y_p[n]. Call your answer w_p[n] and plot it.

( f ) If we convolve x[n] with y_p[n] = x[((−n))N ], how should N be chosen to avoid time-domain aliasing?