Lecture 5 Blog, ECE438 Fall 2014, Prof. Boutin

Friday September 5, 2013 (Week 2) - See Course Outline.

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The goal of this lecture and the next is to illustrate what can happen when one samples pure frequencies. We thus began by introducing the frequencies of the modern western scale. We then 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.

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