Senior Seminar / Final Quarter Chapter 1


Hello everyone. I’m Mike. I’m studying mathematics at University of California at Santa Cruz. This is my last quarter and I have a talk that I have to give, and a senior project that I have to do.  The idea of these posts will be to track my progress on this project, and my progress in my other classes. I hope that this will help motivate me to do my very best in my last year in university.

Here is the class rundown in order of difficulty:
   Senior Seminar
   Real Analysis
   Latin 2
Here is the broad view:
   Senior Seminar:
       Give a 35 minute talk on a mathematical topic, on February 7th
       Turn in a 10 page paper on the topic by the end of the quarter.

    Real Analysis:  
       Weekly homework. Due Wednesdays.

    Latin 2:
       Homework for class 3 times a week.

Listing these is already starting to make things feel more manageable.

Now for some more details on my Senior Seminar:
    I want to study polyphonic source separation algorithms. Through what little research I have done so far I have realized that this is too broad a topic to fit into a 35 minute talk. So, my first task is to narrow down what I will talk about. As it stands right now, maybe a short talk on the Discrete Fourier Transform would be good. Right now, the basic structure might go something like this:

1. Explain in broad terms how digital audio works.  Samples, sampling frequency, possibly the sampling theorem, Nyquist frequency, etc.
2. Explain the mathematics of the Discrete Fourier Transform. Maybe, talk about the Fourier Transforms uses in other branches of math and science.
3. Explain what polyphonic source separation is, and how the Fourier Transform is used as a tool in polyphonic source separation algorithms.

    Somewhere in there I want to talk about psycoacoustics, and cognitive science, but maybe there is not enough time to do that and I will have to save it for the paper.

In conclusion I will leave a list of things that I need to do in the following week:
    Senior Seminar:
       Continue reading Tuomas Virtanen‘s thesis on polyphonic source separation.
       Write a possible outline, and bring it to my professor on Monday.

    Real Analysis:
       Complete homework assignment. Do at least 1 problem every day.
       Finish reading chapter 1. Begin Chapter 2.

       Catch up on backlogged homework. (Tomorrow!)
       Stay caught up. Do a little every day.

Next time I will review my accomplishments, and I will describe a technique developed by my parents to help get ideas down on paper.


One Response to “Senior Seminar / Final Quarter Chapter 1”

  1. Graham says:

    Nice job, Mike. I look forward to your explanation of Virtanen’s approach!

    Smart math students are always needed in {signal processing, theory, algorithms} research.

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