Homework 6, ECE438, Fall 2010, Prof. Boutin
Due in class, Friday October 15, 2010.
The discussion page for this homework is here. Feel free to share your answers/thoughts/questions on that page.
Question 1
Consider the signal
$ x[n]=\cos \left( \omega_1 n \right)+ k \cos \left( \omega_2 n \right) $
where k is a real-valued constant.
a) Write a program that will
- Plot x[n].
- Compute the N point DFT X[k]. (Yes, you may use FFT routines.)
- Plot the magnitude of X[k].
Turn in a print out of your code.
b) Run your program and generate outputs for the cases shown below.
| Case | N | $ \omega_1 $ | k | $ \omega_2 $ |
|---|---|---|---|---|
| 1 | 20 | 0.62831853 | ||
| 2 | 200 | 0.62831853 | 0 | N/A |
| 3 | 20 | 0.64402649 | 0 | N/A |
| 4 | 200 | 0.64402649 | 0 | N/A |
| 5 | 200 | 0.64402649 | 0.2 | 1.27234502 |
| 6 | 200 | 0.64402649 | 0.2 | 0.79168135 |
