(New page: =Homework 4, ECE438, Fall 2011, Prof. Boutin= Due Wednesday October 5, 2011 (in class) ---- ==Questions 1== Compute the DFT of the following signals b) <math class=...) |
|||
| (4 intermediate revisions by 2 users not shown) | |||
| Line 1: | Line 1: | ||
| + | [[Category:ECE438Fall2011Boutin]] | ||
| + | [[Category:ECE438]] | ||
| + | [[Category:ECE]] | ||
| + | [[Category:signal processing]] | ||
| + | [[Category:homework]] | ||
| + | |||
=Homework 4, [[ECE438]], Fall 2011, [[user:mboutin|Prof. Boutin]]= | =Homework 4, [[ECE438]], Fall 2011, [[user:mboutin|Prof. Boutin]]= | ||
Due Wednesday October 5, 2011 (in class) | Due Wednesday October 5, 2011 (in class) | ||
| Line 5: | Line 11: | ||
Compute the DFT of the following signals | Compute the DFT of the following signals | ||
| − | + | a) <math class="inline"> | |
x_1[n] = \left\{ | x_1[n] = \left\{ | ||
\begin{array}{ll} | \begin{array}{ll} | ||
| Line 14: | Line 20: | ||
</math> | </math> | ||
| − | + | b) <math class="inline">x_2[n]= e^{j \frac{\pi}{3} n } \cos ( \frac{\pi}{6} n )</math> | |
| Line 21: | Line 27: | ||
==Question 2 == | ==Question 2 == | ||
| − | Compute the inverse DFT of <math class="inline">X[k]= e^{j \pi k }+e^{j \frac{\pi}{2} k} </math>. | + | Compute the inverse DFT of <math class="inline">X[k]= e^{j \pi k }+e^{-j \frac{\pi}{2} k} </math>. |
| Line 36: | Line 42: | ||
*Note: When asked to compute DFT of a periodic signal x[n], just use the fundamental period of x[n] as N. Same thing for the inverse DFT. -pm | *Note: When asked to compute DFT of a periodic signal x[n], just use the fundamental period of x[n] as N. Same thing for the inverse DFT. -pm | ||
| + | |||
| + | For Q1,b and c, can we just list the complex exponential and say "by comparing to the DFT pairs we can get the answer X[k]=blah" ? | ||
| + | :Yes, you should! -pm | ||
---- | ---- | ||
[[2011_Fall_ECE_438_Boutin|Back to ECE438, Fall 2011, Prof. Boutin]] | [[2011_Fall_ECE_438_Boutin|Back to ECE438, Fall 2011, Prof. Boutin]] | ||
Latest revision as of 02:55, 31 August 2013
Contents
Homework 4, ECE438, Fall 2011, Prof. Boutin
Due Wednesday October 5, 2011 (in class)
Questions 1
Compute the DFT of the following signals
a) $ x_1[n] = \left\{ \begin{array}{ll} 1, & n \text{ multiple of } N\\ 0, & \text{ else}. \end{array} \right. $
b) $ x_2[n]= e^{j \frac{\pi}{3} n } \cos ( \frac{\pi}{6} n ) $
c) $ x_3[n] =(\frac{1}{\sqrt{2}}+j \frac{1}{\sqrt{2}})^n $
Question 2
Compute the inverse DFT of $ X[k]= e^{j \pi k }+e^{-j \frac{\pi}{2} k} $.
Question 3
Under which circumstances can one explicitly reconstruct the DTFT of a finite duration signal from its DFT? Justify your answer mathematically.
Question 4
Prove the time shifting property of the DFT.
Discussion
Write your questions/comments here
- Note: When asked to compute DFT of a periodic signal x[n], just use the fundamental period of x[n] as N. Same thing for the inverse DFT. -pm
For Q1,b and c, can we just list the complex exponential and say "by comparing to the DFT pairs we can get the answer X[k]=blah" ?
- Yes, you should! -pm
