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Jump to [[Lecture1ECE438F13|Lecture 1]], [[Lecture2ECE438F13|2]], [[Lecture3ECE438F13|3]] ,[[Lecture4ECE438F13|4]] ,[[Lecture5ECE438F13|5]] ,[[Lecture6ECE438F13|6]] ,[[Lecture7ECE438F13|7]] ,[[Lecture8ECE438F13|8]] ,[[Lecture9ECE438F13|9]] ,[[Lecture10ECE438F13|10]] ,[[Lecture11ECE438F13|11]] ,[[Lecture12ECE438F13|12]] ,[[Lecture13ECE438F13|13]] ,[[Lecture14ECE438F13|14]] ,[[Lecture15ECE438F13|15]] ,[[Lecture16ECE438F13|16]] ,[[Lecture17ECE438F13|17]] ,[[Lecture18ECE438F13|18]] ,[[Lecture19ECE438F13|19]] ,[[Lecture20ECE438F13|20]] ,[[Lecture21ECE438F13|21]] ,[[Lecture22ECE438F13|22]] ,[[Lecture23ECE438F13|23]] ,[[Lecture24ECE438F13|24]] ,[[Lecture25ECE438F13|25]] ,[[Lecture26ECE438F13|26]] ,[[Lecture27ECE438F13|27]] ,[[Lecture28ECE438F13|28]] ,[[Lecture29ECE438F13|29]] ,[[Lecture30ECE438F13|30]] ,[[Lecture31ECE438F13|31]] ,[[Lecture32ECE438F13|32]] ,[[Lecture33ECE438F13|33]] ,[[Lecture34ECE438F13|34]] ,[[Lecture35ECE438F13|35]] ,[[Lecture36ECE438F13|36]] ,[[Lecture37ECE438F13|37]] ,[[Lecture38ECE438F13|38]] ,[[Lecture39ECE438F13|39]] ,[[Lecture40ECE438F13|40]] ,[[Lecture41ECE438F13|41]] ,[[Lecture42ECE438F13|42]] ,[[Lecture43ECE438F13|43]] ,[[Lecture44ECE438F13|44]] | Jump to [[Lecture1ECE438F13|Lecture 1]], [[Lecture2ECE438F13|2]], [[Lecture3ECE438F13|3]] ,[[Lecture4ECE438F13|4]] ,[[Lecture5ECE438F13|5]] ,[[Lecture6ECE438F13|6]] ,[[Lecture7ECE438F13|7]] ,[[Lecture8ECE438F13|8]] ,[[Lecture9ECE438F13|9]] ,[[Lecture10ECE438F13|10]] ,[[Lecture11ECE438F13|11]] ,[[Lecture12ECE438F13|12]] ,[[Lecture13ECE438F13|13]] ,[[Lecture14ECE438F13|14]] ,[[Lecture15ECE438F13|15]] ,[[Lecture16ECE438F13|16]] ,[[Lecture17ECE438F13|17]] ,[[Lecture18ECE438F13|18]] ,[[Lecture19ECE438F13|19]] ,[[Lecture20ECE438F13|20]] ,[[Lecture21ECE438F13|21]] ,[[Lecture22ECE438F13|22]] ,[[Lecture23ECE438F13|23]] ,[[Lecture24ECE438F13|24]] ,[[Lecture25ECE438F13|25]] ,[[Lecture26ECE438F13|26]] ,[[Lecture27ECE438F13|27]] ,[[Lecture28ECE438F13|28]] ,[[Lecture29ECE438F13|29]] ,[[Lecture30ECE438F13|30]] ,[[Lecture31ECE438F13|31]] ,[[Lecture32ECE438F13|32]] ,[[Lecture33ECE438F13|33]] ,[[Lecture34ECE438F13|34]] ,[[Lecture35ECE438F13|35]] ,[[Lecture36ECE438F13|36]] ,[[Lecture37ECE438F13|37]] ,[[Lecture38ECE438F13|38]] ,[[Lecture39ECE438F13|39]] ,[[Lecture40ECE438F13|40]] ,[[Lecture41ECE438F13|41]] ,[[Lecture42ECE438F13|42]] ,[[Lecture43ECE438F13|43]] ,[[Lecture44ECE438F13|44]] | ||
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| + | Today we reviewed the CTFT of a comb and a rep to clear up the confusion with the notation. We then defined the DT Fourier transform and noted the fact that it is a always a periodic function, with period <span class="texhtml">2π</span>. It was observed that one can thus write any DTFT transform as a "<span class="texhtml">rep<sub>2π</sub></span>" 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. | ||
| + | <br> 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. 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. | ||
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| + | Action items: | ||
| + | *Keep working on the [[HW1ECE38F13|first homework]]. It is due next Friday (in class). | ||
| + | |||
| + | Relevant Rhea pages previously created by students: | ||
| + | *[[Table DT Fourier Transforms|Table of DT Fourier transform pairs and properties]] | ||
<br> Previous: [[Lecture3ECE438F13|Lecture 3]] Next: [[Lecture5ECE438F13|Lecture 5]] | <br> Previous: [[Lecture3ECE438F13|Lecture 3]] Next: [[Lecture5ECE438F13|Lecture 5]] | ||
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[[20113_Fall_ECE_438_Boutin|Back to ECE438 Fall 2013]] | [[20113_Fall_ECE_438_Boutin|Back to ECE438 Fall 2013]] | ||
Revision as of 06:09, 2 September 2013
Lecture 4 Blog, ECE438 Fall 2013, Prof. Boutin
Monday August 26, 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
Today we reviewed the CTFT of a comb and a rep to clear up the confusion with the notation. We then 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 "rep2π" 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. 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.
Action items:
- Keep working on the first homework. It is due next Friday (in class).
Relevant Rhea pages previously created by students:
Previous: Lecture 3 Next: Lecture 5
