Mathematics Department - Math 357 - Topics in Applied Algebra

Math 357 - Topics in Applied Algebra



Prerequisites: Math 250 Introduction to Linear Algebra and Math 251 Multivariable Calculus.


Introduction to Signal and Image Processing by
Discrete Fourier Transform and Wavelet Transforms

This course begins with some topics in linear algebra not covered in Math 250 (such as complex vector spaces, linear transformations, and Fourier series). It then develops the theory of the finite Fourier transform and the new theory of discrete wavelet transforms. These transforms make it possible to separate a digitized audio signal (or two-dimensional image) into low frequency components (coarse outline) and high frequency components (detailed features) in a computationally effective way. Then the signal or image can be compressed or noise can be removed using these components.

The course will involve several MATLAB computer projects. Some prior knowledge of MATLAB is helpful but not necessary. A general familiarity with computers and basic programming skills are needed. Purchase of MATLAB software is not required, since you can use the MATLAB software in the ARC and other public computer labs at Rutgers. We will also use the public-domain wavelet software package Uvi_Wave (which runs under MATLAB).




Schedule Archives

Spring 2014 Schedule

InstructorType Index Section Day(s)/
Period
Time Room
(click for map)
Campus
Goodman, Roe L 05942 01 MTh3 12:00 PM - 1:20 PM ARC-205 BUS


This course is taught during the Spring term.




Texts for the course

1. Lecture notes:
Roe Goodman, Introduction to Signal and Image Processing by Discrete Fourier Transform and Wavelet Transforms
  Download the   pdf file

2. Textbook: (required)
A. Jensen and A. la Cour-Harbo, Ripples in Mathematics: The Discrete Wavelet Transform
Springer   ISBN # 3-540--41662-5
  Buy at Rutgers U. Store or use this link:   Springer




Web Resources




Recommended Books Emphasizing Applications


S. Allen Broughton and Kurt Bryan, Discrete Fourier Analysis and Wavelets
  (not required for course)

James S. Walker, A Primer on Wavelets and Their Scientific Applications (Second Edition)
  (not required for course)




Course Materials




Exams

  • Midterm 1: Thursday, Feb. 27 (ARC 205)
  •   Review session: Wednesday, Feb. 26 at 7:30 pm (Hill 423)
  • Midterm 2: Thursday, April 17 (ARC 205)
  •   Review session: Wednesday, April 16 at 7:30 pm (Hill 423)
  • Final Exam: Thursday, May 8, 8-11 AM (ARC 205)
  •   Review session: Tuesday, May 6 at 3-5 PM (Hill 423)



MATLAB Assignments

  • Project 1: Digital Signals and Vector Graphics   (Due February 10)
        (pdf format)

  • Project 2: Convolution and Discrete Fourier Transform   (Due March 3)
        (pdf format)

  • Project 3: Haar Wavelet Transform   (Due March 24)
        (pdf format)

  • Project 4: Implementation of Wavelet Transforms   (Due April 7)
        (pdf format)

  • Project 5: Image Analysis by Wavelet Transforms   (Due April 28)
  •     (pdf format)
For Projects 4 and 5 you will use the Uvi_Wave collection of Matlab m-files for wavelet transforms from the University of Vigo, Spain. Here are links to download these m-files:

    Uvi_Wave zip file (unzip the file to use the package)

    Uvi_Wave directories and files


Note: You can run Matlab on your own computer (without buying the program) by using the Rutgers X-application server.

  • Click on this apps server link.
  • Log in to the apps server using the connect button at the upper right-hand corner of the screen and your Rutgers NetID.
  • From the Main Menu at the lower left corner of the apps server toolbar, click on Education and then on Matlab
  • From the Main Menu click on Internet and then on Firefox Web Browser to access the Uvi_Wave files from the math 357 course web page.
  • Copy the Uvi_Wave files into a directory that your create on the X-apps server. Then set the Matlab path to this directory.



Course History

Taught by Prof. Goodman 2005-2008, Prof. Retakh 2009, Prof. Goodman 2010-2014.



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