Let x (n) be the input signal to a discrete-time filter with impulse response hi (n) and...

Let x (n) be the input signal to a discrete-time filter with impulse response hi (n) and let y (n) be the corresponding output.

(a) Compute and sketch x(n) and y (n) in the following cases, using the same scale in all figures.

Sketch x (n) , (n) , y₂(n) on one graph and x(n), y₃ (n) , y₄(n), y₅(n) on another graph

(b) What is the difference between yi(n) and y₂(n), and between y₃(n) and y₄(n)?

(c) Comment on the smoothness of y₂(n) and y₄(n). Which factors affect the smoothness?

(d) Compare y₄(n) with n(n) . What is the difference? Can you explain it?

(e) Let Compute y ₆(n) . Sketch x(n), y₂(n), and y ₆(n) on the same figure and comment on the results.