ELE541 Homework Assignment 8

Due April 12, 2001

  1. Find and sketch the output y(n) for a filter with a pulse input x(n) = u(n) - u(n - 6) and the unit pulse response h(n) = 0.8n u(n).

  2. Show that for a filter with h(n) = an u(n), 1/2 < a < 1, the time constant nT of the filter (i.e., the number of samples such that h(nT) approximately equals 1/e) is approximately given by 1/(1-a).

  3. Let the z-transform of h(n) be
    H(z) = (z-1 - z-2)/(1 + z-1)
    1. Sketch the pole/zero diagram.

    2. Find h(n) for all n.

  4. Assume X(z) =(z-2 + 2z-1 + 2)/(z-1 + 1)

    Find x(n)