Instructors: M. L. Giger, C. Metz,
and X. Pan
TA: Payam Seifi
Email: payam {at} uchicago.edu
Text Books
Bracewell: The Fourier Transform
and its Applications
Papoulis: Probability, Random
Variables and Stochastic Processes (Suggested
Schedule
Tuesdays and Thursdays 3:00 to 4:30pm, Sub-basement conference room
(ISB-23).
For the complete schedule, click here.
Office Hours
Tuesdays from 11:00am to 12:00pm at I-129. If you are not sure where it is, here is the map.
Homework
Homework is due one week after the corresponding lecture. You can give them
to me in class, or leave it in my folder in room p-104 before 4:30pm on due
date. For late homework there is 2% penalty per day, which also includes
holidays and weekends. There might be exceptions for the homework that are
extraordinarily hard.
Tips and Suggestions
Here are some survival tips for the Math class:
Try to start working on the
homework from the day they are assigned. This way you will have time to come and
ask me if you don't understand something or you are not sure about your answer.
Of course I might not tell you the answer directly, but I will give you hints
to make sure you are on the right track.
Sometimes you might feel that the
pace of the lectures is very fast. This doesn't make you feel you shouldn't
interrupt by asking your questions. Anyway, if it is still not clear, I will be
more than happy to stay a few minutes after the class to clear it up. Of
course, you can always send me email, though sometimes it might seem more
difficult to put the equations into words than solving them!
It is always a good idea to
discuss the course material and problems with your classmates. However, when it
comes to the written homework, I want your own work. Writing someone else's
solutions is a deadly mistake that you shouldn't even think about!
I will try to post some important
points that you might need to study more carefully after each lecture in the
following section. Of course, this shouldn't mean that you don't need to study
the other parts anyway.
Solve and Enjoy, Have Fun!
Key Points
Lecture One:
If you haven't done yet, try to prove the multiplication-convolution theorem for yourself. This is probabely the most important theorem in the course that you will use repeatedly in the future. It also appears frequently in qualifying exams!
Since you might have worked with Fourier Series (FS) in the past, it is a good exercise to find the relation with Fourier Transform (FT). e.g. what is the FT of a periodic function?
Lecture Two:
The very important part here is that sinusoidal functions are eigenfunctions of a Linear-Shift-Invariant (LSI) system. Do you think this would still be true if we had square waves instead of sinusoids? You might also want to review the proof again. If you like to see a quicker way, try exponential functions instead of sinusoids and take the real part at the end.
Lectures Three and Four:
For extra reading, there is a very nice online book by S. Smith on digital signal processing, which is freely available here:
http://www.dspguide.com/pdfbook.htm
Chapters 8 to 12 cover DFT and FFT. Also sampling theory is covered at chapter 3.
Lectures on linear Algebra:
Many of you were already familiar with the basics of linear algebra. Though here is a free online text by Jim Hefferon that covers the basics:
http://joshua.smcvt.edu/linearalgebra/
For a review of SVD, you might want to look at the article in Wikipedia:
http://en.wikipedia.org/wiki/Singular_value_decomposition