Eleg333 signals and systems homework - determine the

Question

Signals And Systems Homework -

Q1. Determine the response of the following systems to the input signal

X(n) = |n| for -3<= n <= 3

Otherwise, X(n) = 0

(a) y(n) = x(n)

(b) y(n) = x(n - 1)

(c) y(n) = x(n + 1)

(d) y(n) = (1/3)[x(n + 1) + x(n) + x(n - 1)]

Q2. Make a block diagram to represent:

y(n) = 0.25y(n - 1) + 0.5x(n) + 0.5x(n - 1)

Q3. Let x(n) be the input signal to a discrete-time filter with impulse response h_i(n) and let y_i(n) be the corresponding output.

(a) Compute and sketch x(n) and y(n) in the following cases. Hint: y(n) = x(n) * h(n)

Sketch x(n), y₁(n), y₂(n) on one graph and x(n), y₃(n), y4(n), y₅(n) on another Graph

(b) What is the difference between y₁(n) and y₂(n) and between y₃(n), y₄(n)?

(c) Compare y₄(n) with y₅(n). What is the difference? Can you explain it?