Latest revision as of 04:39, 8 September 2014

Lecture 4 Blog, ECE438 Fall 2014, Prof. Boutin

Wednesday September 3, 2013 (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

In the fourth lecture, we finished computing the Fourier transform of a rep, and we computed the Fourier transform of a comb. 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 " $rep 2π$ " 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.

Action items:

Finish the first homework. It is due Friday (in class).
Pick your slecture topic.

Relevant Rhea pages:

Table of DT Fourier transform pairs and properties

Previous: Lecture 3 Next: Lecture 5

Back to ECE438 Fall 2014

@@ Line 11: / Line 11: @@
 Jump to [[Lecture1ECE438F14|Lecture 1]], [[Lecture2ECE438F14|2]], [[Lecture3ECE438F14|3]] ,[[Lecture4ECE438F14|4]] ,[[Lecture5ECE438F14|5]] ,[[Lecture6ECE438F14|6]] ,[[Lecture7ECE438F14|7]] ,[[Lecture8ECE438F14|8]] ,[[Lecture9ECE438F14|9]] ,[[Lecture10ECE438F14|10]] ,[[Lecture11ECE438F14|11]] ,[[Lecture12ECE438F14|12]] ,[[Lecture13ECE438F14|13]] ,[[Lecture14ECE438F14|14]] ,[[Lecture15ECE438F14|15]] ,[[Lecture16ECE438F14|16]] ,[[Lecture17ECE438F14|17]] ,[[Lecture18ECE438F14|18]] ,[[Lecture19ECE438F14|19]] ,[[Lecture20ECE438F14|20]] ,[[Lecture21ECE438F14|21]] ,[[Lecture22ECE438F14|22]] ,[[Lecture23ECE438F14|23]] ,[[Lecture24ECE438F14|24]] ,[[Lecture25ECE438F14|25]] ,[[Lecture26ECE438F14|26]] ,[[Lecture27ECE438F14|27]] ,[[Lecture28ECE438F14|28]] ,[[Lecture29ECE438F14|29]] ,[[Lecture30ECE438F14|30]] ,[[Lecture31ECE438F14|31]] ,[[Lecture32ECE438F14|32]] ,[[Lecture33ECE438F14|33]] ,[[Lecture34ECE438F14|34]] ,[[Lecture35ECE438F14|35]] ,[[Lecture36ECE438F14|36]] ,[[Lecture37ECE438F14|37]] ,[[Lecture38ECE438F14|38]] ,[[Lecture39ECE438F14|39]] ,[[Lecture40ECE438F14|40]] ,[[Lecture41ECE438F14|41]] ,[[Lecture42ECE438F14|42]] ,[[Lecture43ECE438F14|43]] ,[[Lecture44ECE438F14|44]]
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-In the fourth lecture, we began by observing how the scaling property of the Dirac delta can be used to simplify Fourier transform expressions involving Dirac deltas. We then defined the "rep" and "comb" operators. We finished the lecture by computing the Fourier transform of a rep, but we did not quite finish the computation.
+In the fourth lecture,  we finished computing the Fourier transform of a rep, and we computed the Fourier transform of a comb. 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 "<span class="texhtml">rep<sub>2π</sub></span>" 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.
 Action items:
-*Begin working on the  [[HW1ECE38F14|first homework]]. It is due next Friday (in class).
+*Finish the  [[HW1ECE38F14|first homework]]. It is due Friday (in class).
+*Pick your slecture topic.
 Relevant Rhea pages:
-*[[Homework_3_ECE438F09|About scaling of the Dirac Delta]]
+*[[Table DT Fourier Transforms|Table of DT Fourier transform pairs and properties]]
 Previous: [[Lecture3ECE438F14|Lecture 3]]

Difference between revisions of "Lecture4ECE438F14" - Rhea

Latest revision as of 04:39, 8 September 2014

Lecture 4 Blog, ECE438 Fall 2014, Prof. Boutin

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