Digital Signal Processing Assignment 2

Submit the assignment in the usual format.

  1. Do Mitra problems 2.36 and 2.38 and 2.41.

  2. Do Mitra problems 2.50, 2.51, and 2.52.

  3. We are given the two sequences x = [1 -3 1 5] and w = [7 -7 -9 -3]. Does there exist a sequence y of length 4 such that the circular convolution of x with y equals w? If so, find y; if not, show why such y does not exist.

  4. Write a Matlab routine to find the circular convolution of two sequences, by means of linear convolution (using the Matlab routine conv). Demonstrate the operation of your routine on the sequences x = [ 1 2 3 4] and y = [-1 2 1 -1].

    The following exercises involve continuous convolutions. However, they should provide useful review and practice.

  5. Use Matlab to plot the following convolutions:
    1. p(x) = rect(x) * rect(x-2)
    2. r(x) = rect(x) * rect(x/4)

  6. Perform the following convolutions analytically and plot the results. You may use Matlab for plotting.
    1. f(x) = step(x) * step(x)
    2. g(x) = step(x) * rect(x)
    3. h(x) = step(x) * tri(x)

  7. Given an LSI system with impulse response h(x) = exp(-x)step(x), find gi(x) = fi(x) * h(x) for each of the following input signals fi(x). Plot both input and output signals (you may use Matlab for the plots).
    1. f1(x) = step(x-5)
    2. f2(x) = rect(10x-0.5)
    3. f3(x) = rect(0.1x-0.5)
    4. f4(x) = d(x+0.1)- d(x-0.1)

Maintained by John Loomis, last updated 30 Aug 2005