Lecture 4 Blog, ECE438 Fall 2015, Prof. Boutin
Monday August 31, 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 .
Today we showed that the CTFT of a "comb" of a signal is a "rep" of the CTFT of the signal. We then began the second topic: "Spectral representation of DT signals". After giving the formulas for the DTFT and the inverse DTFT, we observed the periodicity property of the DTFT and observed that one can thus write any DTFT transform as a "rep2π" function. We also obtained the DTFT of a complex exponential. We observed 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.
Relevant Rhea pages:
- Table of DT Fourier transform pairs and properties
- Definition of the "rep" and "comb" operators:
- Text slecture by Xiaozhe Fan
- Fourier transform of "rep" and "comb":
- Video slecture by Ben Capano
- Text slecture by Matt Miller
Action Items
- Finish HW1. It is due Wednesday September 2, 2015
Questions/Comments
- Post question here
Previous: Lecture 3
Next: Lecture 5
