MATH 750
Fourier Analysis

   Homework Assignments
    

No.	Due	Assignment
#0	Tuesday Aug. 29.	Download the write-up and matlab demo script. Run the demo code to observe the experiment described in class on Thursday. Matlab should be available from your graduate student account. Let me know if you have trouble running this demo, which is to illustrate two modes of convergence of Fourier series, as well as rates and qualitative behavior. Although matlab programing not required for this assignment, you can find a quick tutorial on matlab here and a little more detail at this link.
#1	Thursday Sept. 7.	PDF of HW #1 is here
#2 (text)	Thursday Sept. 21	Pg 7, Sec. 1:   #1 (b-d), 3, 4, 6, 7, 8 Pg 17, Sec. 2:  #4

   Worksheets

Matlab Tutorials and Documentation

For a demonstration of the simple syntax and broad functionality of Matlab, first start Matlab by clicking the Matlab icon on the XP machines or by typing "matlab" at the prompt on the UNIX machines. Once the application is launched, at the MATLAB prompt type the command "demo". From the menu which will be displayed, run the demos that interest you by following the instructions on the screen.

You can find helpful tutorials and quick-start documents at the following links:

1. Manual of basics to get started (University of Florida): MatLab Primer
2. A quick detailed reference from the University of Dundee. (This is a keeper!)
3. "Getting Started with Matlab" from MathWorks in hyperlinked, cross-referenced PDF document format [Getting Started] and on-line at the URL [On-Line]
4. Official Matlab source PDF documents for technical information from MathWorks.


Minimalist Matlab m-files
Download the Matlab m-files from the following table and save them in your "working directory".



Title	Brief Descripton
Fourier_Cesaro.m	Comparison of qualitative properties and convergence of Fourier and Cesaro sums.
Dirichlet.m	Animated plot of the Dirichlet kernel.
FejerKernels.m	Animated plot of the Fejer kernels.
Java applet link	Simple application to illustrate the concept of aliasing when using digital approximations to Fourier signals.
Digital Audio Tutorial	Tutorial on Digital Audio processing: harmonic tones, amplitudes, sampling rates, Nyquist theorem, and A2D quantization (analogue to digital conversion).
AmplitudeModulation.m	Example of an AM (Amplitude Modulated) signal.
FrequencyModulation.m	Example of an FM (Frequency Modulated) signal.
PureTones.m	Example of a pure harmonic, increasing by 1/8 notes. Notice the clicks between notes, indicating discontinuities.
Disconsonace.m	m-file illustrating 'beats' formed from two signals of nearly equal frequencies; by uncommenting commands, also illustrates auditory effects of nonlinear phase.
PDF of Math Music	Write-up of description of Fourier analysis and Music. Prepared by Mark Peterson of the University of Colorado (available at http://amath.colorado.edu/pub/matlab/music/MathMusic.pdf).

This page maintained by Robert Sharpley (sharpley@math.sc.edu) and last updated Aug. 31, 2006.  This page ©2006-2007, The Board of Trustees of the University of South Carolina.  URL: http://www.,math.sc.edu/~sharpley/math750