| Line 11: | Line 11: | ||
Consider the signal | Consider the signal | ||
| − | < | + | <math>x[n]=\cos \left( \omega_1 n \right)+ k \cos \left( \omega_2 n \right) </math> |
| − | where k is a real valued constant. | + | where k is a real-valued constant. |
a) Write a program that will | a) Write a program that will | ||
| Line 25: | Line 25: | ||
b) Run your program and generate outputs for the cases shown below. | b) Run your program and generate outputs for the cases shown below. | ||
| − | {| width="200" border="1" cellpadding=" | + | {| width="200" border="1" cellpadding="5" cellspacing="1" |
|- | |- | ||
! scope="col" | Case | ! scope="col" | Case | ||
| Line 35: | Line 35: | ||
| 1 | | 1 | ||
| 20 | | 20 | ||
| − | | | + | | 0.62831853 |
| | | | ||
| | | | ||
| Line 41: | Line 41: | ||
| 2 | | 2 | ||
| 200 | | 200 | ||
| − | | | + | | 0.62831853 |
| − | | | + | | 0 |
| − | | | + | | N/A |
|- | |- | ||
| 3 | | 3 | ||
| 20 | | 20 | ||
| − | | | + | | 0.64402649 |
| − | | | + | | 0 |
| − | | | + | | N/A |
|- | |- | ||
| 4 | | 4 | ||
| 200 | | 200 | ||
| − | | | + | | 0.64402649 |
| − | | | + | | 0 |
| − | | | + | | N/A |
|- | |- | ||
| 5 | | 5 | ||
| 200 | | 200 | ||
| − | | | + | | 0.64402649 |
| − | | | + | | 0.2 |
| − | | | + | | 1.27234502 |
|- | |- | ||
| 6 | | 6 | ||
| 200 | | 200 | ||
| − | | | + | | 0.64402649 |
| − | | | + | | 0.2 |
| − | | | + | | 0.79168135 |
|} | |} | ||
Revision as of 08:20, 8 October 2010
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 |
