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Undergraduate

Syllabus

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

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.

DateLectureTexbook SectionTopics
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 z-transform
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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Department of Mathematics

Department of Mathematics
Rutgers University
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