Lecture 5 Blog, ECE438 Fall 2015, Prof. Boutin
Wednesday September 1, 2015 (Week 2) - 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, 45 .
The goal of today's lecture was to illustrate what can happen when one samples a pure frequency. We considered a CT signal representing a middle C (a pure frequency) and sampled that signal 1000 times per second. We asked ourselves what is the relationship between the CTFT of the pure frequency and the DTFT of the sampling of that signal. To answer that question, we first computed the CTFT of signal and the DTFT of its sampling. It was observed that this sampling yields a DT signal that also sounds like a middle C. Perhaps the most confusing part of the demonstration was when we pulled out the factor 1000 in front of the Dirac deltas. The reason why we did this will become clearer once we see the general relationship between the CTFT of a signal and the DTFT of a sampling of that signal. If you are still confused about that property of the Dirac deltas, please take a look at this page.
We then considered another signal (a higher C) and sampled it with the same frequency as for the middle C (1000 times per seconds). We did not quite finish obtaining the DTFT of the sampling, but we could already observe that aliasing was occuring. We will finish the discussion on Friday.
Relevant Rhea pages:
- ECE301 students playing music with MATLAB.
- About the Discrete-time Fourier transform (DTFT) of a sampled cosine:
- Text slecture by Andrew Pawling
- Text slecture by Sutton Hathorn
- Text slecture by Sahil Sanghani
- Text slecture by Yijun Han
Action Items
- Begin working on HW2. It is due Wednesday September 9, 2015
Questions/Comments
- Post question here
Previous: Lecture 4
Next: Lecture 6
