Digital Signal Processing Assignment 2
Submit the assignment in the usual format.
- Do Mitra problems 2.36 and 2.38 and 2.41.
- Do Mitra problems 2.50, 2.51, and 2.52.
- 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.
- 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.
- Use Matlab to plot the following convolutions:
- p(x) = rect(x) * rect(x-2)
- r(x) = rect(x) * rect(x/4)
- Perform the following convolutions analytically and plot the results.
You may use Matlab for plotting.
- f(x) = step(x) * step(x)
- g(x) = step(x) * rect(x)
- h(x) = step(x) * tri(x)
- 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).
- f1(x) = step(x-5)
- f2(x) = rect(10x-0.5)
- f3(x) = rect(0.1x-0.5)
- f4(x) = d(x+0.1)-
d(x-0.1)
Maintained by John Loomis,
last updated 30 Aug 2005