640:357 Topics in Applied Algebra (Spring, 2017)
Introduction to Signal and Image Processing by
Discrete Fourier and Wavelet Transforms
Textbook for the course:
Discrete Fourier and Wavelet Transforms by Roe W. Goodman
Available in hard cover, paperback, and e-book format. Go to
World Scientific Publishing
Syllabus
There is a 10-minute quiz at the end of each Thursday class meeting, except when there is a midterm exam. This is indicated by Q in the syllabus. The first quiz is diagnostic, and does not count for the course grade.
| Date | Lecture | Texbook Section | Topics |
|---|---|---|---|
| 1/19 | 1Q | 1.2, 1.3 | Sampling and Quantization Vector Spaces |
| 1/23 | 2 | 1.4, 1.5.1 | Bases and Dual Bases; Linear Transformations and Matrices |
| 1/26 | 3Q | 1.5.2, 1.5.3, 1.6 | Direct Sums, Partitioned Matrices; Vector Graphics |
| 1/30 | 4 | 1.7 | Inner Products, Orthogonal Projections, and Unitary Matrices |
| 2/02 | 5Q | 1.8 | Fourier Series |
| Due: | 2/06 | Course web page | MATLAB Project #1: Digital Signals and Vector Graphics |
| 2/06 | 6 | 2.2 | Sampling and Aliasing |
| 2/09 | 7Q | 2.3 | Discrete Fourier Transform and Fourier Matrix |
| 2/13 | 8 | 2.4.1, 2.4.2 | Shift-Invariant Transformations and Circulant Matrices |
| 2/16 | 9Q | 2.4.3, 2.5 | Circular Convolution and Filters |
| 2/20 | 10 | 2.6 | Downsampling and Fast Fourier Transform |
| 2/23 | 11 | Exam 1 | (closed book) |
| Due: | 2/27 | Course web page | MATLAB Project #2: Convolution and Discrete Fourier Transform |
| 2/27 | 12 | 3.2.1, 3.2.2 | Haar Wavelet Transform; Prediction and Update Transforms |
| 3/02 | 13Q | 3.3.1, 3.3.2 | Multiple Scale Haar Wavelet Transforms; Signal processing |
| 3/06 | 14 | 3.4.1, 3.4.2 | Wavelet Transforms for Periodic Signals by Lifting
CDF(2, 2) and Daub4 wavlet transforms |
| 3/09 | 15Q | 3.5 | Wavelet Bases for Periodic Signals |
| Spring Break | |||
| Due: | 3/20 | Course web page | MATLAB Project #3: Haar Wavelet Transform |
| 3/20 | 16 | 3.6.1, 3.6.2 | One-scale 2D Wavelet Transforms |
| 3/23 | 17Q | 3.6.3, 3.6.4 4.2.1 |
Multiscale 2D Wavelet Transforms and Image Compression Signals and z-transforms |
| 3/27 | 18 | 4.2.2, 4.2.3, 4.2.4 | Convolution; Shift-Invariant Filters Downsampling and Upsampling |
| 3/30 | 19Q | 4.2.5, 4.2.6, 4.2.7 | Filtering and Downsampling Periodic Signals Discrete Fourier Transform and |
| Due | 4/03 | Course web page | MATLAB Project #4: Implementation of Wavelet Transforms |
| 4/03 | 20 | 4.3 | Filter Banks and Polyphase Matrices |
| 4/06 | 21Q | 4.4.1, 4.4.2 | Filter Banks and Modulation Matrices Lowpass and Highpass Filters |
| 4/10 | 22 | 4.4.3, 4.5.1 | Perfect Reconstruction Filter Banks |
| 4/13 | 23 | Exam 2 | (closed book) |
| 4/17 | 24 | 4.5.2, 4.5.3 | Lowpass Filters and Bezout polynomials; CDF(p, q) filters |
| 4/20 | 25Q | 4.6 4.7 |
Comparison Polyphase and Modulation Matrices Lifting Step Factorization of Polyphase Matrices |
| Due: | 4/24 | Course web page | MATLAB Project #5: Image Analysis by Wavelet Transforms |
| 4/24 | 26 | 4.8 | Biorthogonal Wavelet Bases |
| 4/27 | 27Q | 4.9 4.10.1 |
Orthogonal Filter Banks Power Spectral Response Function |
| 5/01 | 28 | 4.10.2, 4.10.3 | Construction of the Daub4 and Daub2K Filters |
| 5/04 | 8-11 AM | Final Exam | closed book--formula sheet provided |
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Revised November 30, 2016