Lecture 3 Blog, ECE438 Fall 2011, Prof. Boutin

Friday August 26, 2010 (Week 1) - See Course Outline.

In the third lecture, we obtained the CT Fourier transform of the "comb" and "rep" functions. We also defined the DT Fourier transform and noted the fact that it is a always a periodic function, with period 2π. It was observed that one can thus write any DTFT transform as a "rep_2π" function. We showed that it is not wise to attempt to Fourier transform a complex exponential using the definition, but we found a way around that problem by using the inverse Fourier transform formula to guess the answer.

In preparation for the next lecture, in which we will illustrate what can happen when on samples pure frequencies, we introduced the frequencies of the modern western scale.

Action items:

• Solve the following two practice problems on the DTFT
  • What is the Fourier transform of this DT cosine?
  • What is the Fourier transform of this DT rect function?
• Keep working on the first homework. It is due next Wednesday (in class).

Relevant Rhea pages previously created by students:

• Table of DT Fourier transform pairs and properties

Previous: Lecture 2 Next: Lecture 4