Lecture 16 Blog, ECE438 Fall 2013, Prof. Boutin
Wednesday September 25, 2013 (Week 6) - See Course Outline.
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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).
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