Discrete-Time Convolution:
Write a MATLAB program that calculates the discrete convolution sum of two discrete-time sequences of nite length.
input: two arrays and their rst time indices with non-zero values (lengths, if necessary).
output: resulting array and its rst time index with non-zero value (length, if necessary). You may limit the index of the input arrays to the interval [ 100; 100] and the output array
to the interval [ 200; 200]. Make sure there are no out-of-bound index errors.
Given two discrete-time sequences x1[n] and x2[n] as below, nd the results of the convolu-tions: x1[n] x1[n]; x2[n] x2[n], and x1[n] x2[n]:
1)
x1
[n] =
8
1; if 0 n 19
and
x2[n] =
8
j
n
; if
n
5
>
5;
if 20
n
39
j
j j
>
<
<
>
:
0;
otherwise
>
0;
otherwise
>
>
:
2)
x1
[n] = u[
2n + 4]
u[
n 3]
and
x2[n] = 7 [
n
10]
14 [ n + 10]
3)
x1
[n] =
8
10 e
nj;
if jnj 25
and
x2[n] = 4 [n + 3]
8 [n] + 4 [n 3]
<
0;
otherwise
:
Plot the sequences and the convolution results using the stem( )command in MATLAB. Please do not use the conv( ) command in MATLAB. You may only use it to cross-check
your results.
Submit the results of your own work in the form of a well-documented report on Moodle. Borrowing full or partial code from your peers or elsewhere is not allowed and will be punished. Please include all evidence (plots, screen dumps, MATLAB codes, MATLAB command window print-outs, etc.) as needed in your report. Append your MATLAB code at the end of your assignment, do not upload it separately. The axes of all plots should be scaled and labeled. Typing your report instead of handwriting some parts will be better. Please do not upload any photos/images of your report. Your complete report should be uploaded on Moodle as a single good-quality pdf le by the given deadline. Please try to upload several hours before the deadline to avoid last minute problems that may cause you to miss the deadline. Please DO NOT submit any hardcopies or les by e-mail or on memory stick/CD.
