Revision as of 04:28, 29 December 2010

Lecture Blog, ECE438, Fall 2010, Prof. Boutin

Please do not edit this page. If you want to add/remove something, just copy the code on a new page and edit only that new page. -pm

Lecture 1

Lecture 1 Blog, ECE438 Fall 2010, Prof. Boutin

Monday August 23, 2010 (Week 1) - See Course Outline.

In the first lecture, we covered the syllabus and gave a short introduction to Rhea. We then talked about what is "Digital Signal Processing". In particular, we discussed the two following applications:

• Historical Preservation: Original Caruso (1904) versus Caruso digitally processed
• A software to remove the sound of vuvuzelas at World Cup of Soccer, 2010.

The actual material covered was very similar the material of the first lecture of Fall 2009. Lecture notes for that lecture are here. (These would be a very good starting point in case you were thinking of typing the notes and sharing them on Rhea.)

Action items for students include

• Read Rhea's disclaimer.
• Read the ECE438 Peer legacy page and consider contributing to other peer legacy pages, such as ECE201, ECE202, ECE301, and EPICS.

The main goal of this lecture was to clarify the course policies and get everybody excited about the subject!

Next: Lecture 2

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Lecture 2

Lecture 2 Blog, ECE438 Fall 2010, Prof. Boutin

Wendesday August 25, 2010 (Week 1) - See Course Outline.

In the second lecture, we introduced the CT Fourier transform in terms of frequency "f" and discussed its relationship with the frequency transform in terms of $ \omega $. The "rep" and "comb" functions were introduced. Some subtleties regarding the rescaling of the Dirac delta were observed. The first homework was announced. It is due next Wednesday.

Idea: How about a couple of you take this table of CTFT and make a new one in terms of f?

Relevant Rhea pages created by students last fall:

• About the CTFT in terms of f and its properties
• About scaling of the Dirac Delta
• About the Rep and Comb function
• Summary of CT and DT Fourier transforms

Do you see any mistake in these pages? Do you have questions? Feel free to write directly on these pages, expand them, or write new pages.

Previous: Lecture 1; Next: Lecture 3

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Lecture 3

Lecture 3 Blog, ECE438 Fall 2010, Prof. Boutin

Friday August 27, 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 computed the DTFT of a complex exponential.

Students do not seem at all happy about the switch from frequency in radians per time unit to frequency in hertz...

Previous: Lecture 2; Next: Lecture 4

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Lecture 4

Lecture 4 Blog, ECE438 Fall 2010, Prof. Boutin

Monday August 30, 2010.

In the fourth lecture, we obtained the frequencies of the notes in the middle scale of a piano. We then computed the CTFT of signal that would "sound" like a middle C and the CTFT of a signal that would "sound" like the next higher C. We also obtained the DTFT of a sampling of each of these signals (using the same sampling frequency). It was observed that, while the sampling of middle C yields a DT signal that also sounds like a middle C, the sampling of the higher C does not at all sound like a C.

Relevant links:

• ECE301 students playing music with MATLAB.

Seems like students have little recollection of the sampling material from ECE301. We shall fix this!

Any comments/questions? Please write them below.

Previous: Lecture 3; Next: Lecture 5

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Lecture 5

Lecture 5 Blog, ECE438 Fall 2010, Prof. Boutin

Wednesday September 1, 2010.

In the fifth lecture, we collected the first homework assignment and announced the second homework assignment. It was noted that the student's presentation of the first homework is less than desirable. As a result, it was announced that the second homework would be graded by double-blind peer review.

We finished our discussion of aliasing when sampling pure frequencies. It is highly suggested that students review the periodicity of discrete-time complex exponentials (including the concept of harmonics).

References

• "Signals and systems", by Oppenheim, Wilsky, and Nawab, Section 1.3.3.

We defined the z-transform and highlighted its relationship with the DTFT. We also computed the z-transform of a signal for which the Fourier transform does not exist. The first student who creates a table of z-transform on Rhea with at least 15 signals will get a 0.5% bonus. (You must use the same format as the one use for this table of Laplace transforms.)

Related links:

• A student summary of the z-transform and its properties

Please feel free to correct the material on these pages, comment on them, or write new/better ones.

Any comments/questions? Please write them below.

Previous: Lecture 4; Next: Lecture 6

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Lecture 6

Lecture 6 Blog, ECE438 Fall 2010, Prof. Boutin

Friday September 3, 2010.

In Lecture #6, we talked about the ROC of the z-transform but we did not have time to cover the inverse z-transform. I just realized that Monday is off, so this means we will not have time to cover the inverse z-transform before the homework is due. Therefore, I will make a change in the second homework and make the computation of the inverse z-transforms part of homework number 3.

In case you want to get a head start, here are the notes on the inverse z-transform from Fall 2009 and here is another version. (Note that these were written by students, so I make no guarantee regarding the content..)

Previous: Lecture 5; Next: Lecture 7

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Lecture 7

Lecture 7 Blog, ECE438 Fall 2010, Prof. Boutin

Wednesday September 8, 2010.

In Lecture #7, we talked about convergence of the z-transform at infinity. We also talked about the time-shifting property of the z-transform. Finally, we gave an explicit formula for the inverse z-transform, and described a straightforward procedure for computing it using power series. If you do not feel completely comfortable with the geometric series, this is a good time to brush up on the subject.

Related Rhea pages (please feel free to comment/discuss directly on these pages):

• Some tricks to deal with the geometric series (from William Schmidt)
• Yes, the geometric series also holds for complex numbers!
• Be careful if the argument is equal to one!!!
• Please consider writing a page on the geometric series! (You will get up to 0.5% bonus points for doing so, depending on the quality/content.)

The third homework is due next Wednesday. It basically consists in computing the inverse z-transforms of the signal you used in HW2 and in doing the peer review of HW2.

Did everybody hand in their homework 2 in the "Assignment 2" box in Prof. Mimi's dropbox? Note that this is NOT the same as Prof. Mimi's dropbox.

Previous: Lecture 6; Next: Lecture 8

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Please do not edit this page. If you want to add/remove something, just copy the code on a new page and edit only that new page. -pm