Time and Location: T, Th 1:00 – 2:30, rm 412

Professor: Douglas Wiens, McDonnell Hall 403, x-6517

Texts:

The course will consist of two basic sections: the first devoted to analysis of digital time series or spatial data and the second to inverse theory. Most subjects discussed in the first section can be found in Lynn's textbook, subjects discussed in the second section will largely follow Menke. Most of the examples I will use will come from seismology, but students are encouraged to bring up examples of signal analysis or inverse problems from potential fields, remote sensing and other disciplines. I plan to cover the following subjects:

1) Basic concepts: Fourier Transforms, delta functions, sampling (Lynn, ch 2-3)

2) Linear system theory, convolution, time & frequency resolution (Lynn, ch 7,8)

3) Analog systems; analog filters (Lynn, ch 3, 9)

4) Discrete Fourier Transform, Fast Fourier Transform, Z Transform (Lynn, ch 4)

5) Digital filters and their properties (Lynn, ch 9)

7) Deconvolution, Inverse Filters

8) Introduction to Inverse problems (Menke, ch 1)

9) The Least Squares approach to Gaussian, linear problems (Menke, ch 2-3)

10) Generalized Inverses (Menke, ch 4)

11) Uniqueness of solutions; vector spaces (Menke, ch 6-7)

12) Non-Gaussian and Non-linear inverse problems (Menke, ch 8-9)

Grades: Students will be required to complete several problem sets, some involving computer work. A final project will also be required.