This is a site listing some of the code I have written

These are annotated follow-ups to the homeworks from Professor Kutz's 481/581 course. I made the computation part p-code (which I normally despise!!!) in case the homeworks are re-used in the future.

• Fourier Methods
  • A basic, brute-force DFT that has a lot of print outs. (sws, published)
  • A cool tool that uses SAGE's symbolic functions to show Fourier modes in a given domain.(html , sws)
    • The homework assignment that inspired it! I don't think this is what Professor Tung had in mind when he wanted to teach us Fourier integrals. This shows SAGE output to TeX. ()
    • Also another use in a calculus of variations assignment.
  • The same as above but a dimension higher. (May run slow if you have a netbook like me!)
• Wavelets/Signal Processing
  • I played aroud with some Wavelet stuff from Yves Nievergelt's book. (published, sws)
• After taking a course where I learned about Curvilinear Coordinates, I have wanted to make a little SAGE tool to be able to take arbitrary orthogonal coordinate systems and create 'graph paper' from the transformation formulas. From there, I would like to be able to export this into SVD files. I am hoping that this would make learning about these systems more interesting and easy.
• My group's project (Notebook, Paper by Matt Junge) from taking Professor Stein's 481 course. We investigated using SAGE for a very brute force demonstration of the 'Ham Sandwich Theorem' in the plane.
• My individual project from Professor Stein's 581 course. I investigated FFTs and what is used in SAGE. In the course of this, I learned all about different algorithms, including Rader's, Bluestein's, Short time, Real-time, and found it fascinating. For an in-depth look, I highly recommend taking a look at FFT Black Box book. Take a look at the course, since I earned a 3.9 and thus should be considered a reasonable resource for questions!
• Complex Numbers
  • Some examples of complex color plots (html, sws).
• Symbolic Evaluation of the Euler-Lagrange functional for a variety of surfaces.

(html, sws)

• Curvelets
  • I investigated curvelets for Professor Kutz following my project in his 482/582 class (final paper). I continued this in Professor Yongmin Kim's EE 568 graduate image processing course (final presentation).
• Tours
  • As part of my research, I made a tour showing decompositions using various transforms and operations on them. This code is a pain to transfer because of all the packages!!!
  • Some basic operations using curvelets, in the spirit of Peyre (huge help to me!)
  • Fourier Tour. This should help you understand the 2d Fourier transform.
• K-SVD/SVD
  • A little demonstration showing how both can be used to generate basis sets.