Lecture 14 Blog, ECE438 Fall 2013, Prof. Boutin
Wednesday September 25, 2013 (Week 6) - See Course Outline.
Jump to Lecture 1, 2, 3 ,4 ,5 ,6 ,7 ,8 ,9 ,10 ,11 ,12 ,13 ,14 ,15 ,16 ,17 ,18 ,19 ,20 ,21 ,22 ,23 ,24 ,25 ,26 ,27 ,28 ,29 ,30 ,31 ,32 ,33 ,34 ,35 ,36 ,37 ,38 ,39 ,40 ,41 ,42 ,43 ,44
Today we talked about upsampling. More specifically, we derived the relationship between the DTFT of $ x_2[n] $ and the DTFT of $ x_1[n] $ when
$ x_2[n]=\left\{ \begin{array}{ll} x_1[n/D], & \text{ when }n/D \text{ is an integer, }\\ 0, & \text{ else.} \end{array} \right. $
for some positive integer D. We then concluded that, in order to obtain the resampling $ x_3[n]=x(T_2n) $, we need to assume that x(t) was band-limited with $ f_{max}<\pi /D $ and apply a low-pass filter with gain D and cut-off $ \pi/D $ to $ x_2[n] $.
Action Items
- Keep working on the fifth homework. It's due Friday.
- Continue preparing for the first test:
- Review the relationship between a sampling and a downsampling (in the frequency domain).
Previous: Lecture 15 Next: Lecture 17
