Transform Theory and Signals

Faculty members: Frank Neubrander, Gestur Olafsson, and P. Sundar.

The course work's goal is to provide the student a working knowledge in analysis, transform theory, and applied harmonic analysis, and show how these tools are used in applied problems. Here transform theory includes: Fourier series and integrals, the Fast Fourier transform, the z-transform, the Radon transform, and wavelet transforms.

To be successful in this program, the student needs a firm foundation in analysis. The minimal requirement of three 7000 level classes in mathematics should include Real Analysis (Math 7311) and Harmonic analysis and Wavelet theory (now listed under Math 7390, Seminar in Analysis). Further courses related to this topic are: Math 4325 Fourier Analysis, Math 7320 Ordinary Differential Equations, Math 7330 Functional Analysis, Math 7350 Complex Analysis, and Math 7360 Probability Theory.

Other offerings in the Department of Mathematics having significant benefit to students in transform theory and signal analysis:

1. Math 4036/7350: Complex Variables
2. Math 4038: Mathematical Methods in Engineering
3. Math 4065/66: Numerical Analysis I/II

There are several courses in other departments significantly related to the program. Amongst these are:

1. EE 4150: Digital Signal Processing.
2. EE 4780: Introduction to computer vision
3. EE 7150: Theory and Application of Digital Signal Processing
4. EE 7730/40: Image Analysis I/II
5. PHYS 4112: Intermediate Mathematical Physics
6. PHYS 7211/7212: Mathematical Methods of Theoretical Physics