Calendar

The course grade is based primarily on the class project (presentation + final report). Approximate breakdown: Project: 90%, Homework: 10%.

READINGS refer to the Text: Strang and Nguyen. Wavelets and Filter Banks. Wellesley-Cambridge Press, 1997.

LECTURE NOTES: Slides open as color slides in a pdf document. Handouts open as black-and-white slides in a pdf document. To view the lecture slides properly, you might need special fonts. If this happens, please refer to the handouts instead, which have all the fonts embedded in them and can be viewed or printed as-is.

SES # TOPICS READINGS LECTURE NOTES ASSIGNMENTS
1 Discrete-time Filters: Convolution; Fourier Transform; Lowpass and Highpass Filters Sec 1.1-1.4, 2.1

Slides (PDF)Handouts (PDF)

2 Sampling Rate Change Operations: Upsampling and Downsampling; Fractional Sampling; Interpolation Sec 3.1-3.3

Slides (PDF)Handouts (PDF)

3 Filter Banks: Time Domain (Haar example) and Frequency Domain; Conditions for Alias Cancellation and no Distortion Sec 4.1

Slides (PDF)Handouts (PDF)

HW 1 out (PDF)
4 Filter Banks (contd.): Perfect Reconstruction; Halfband Filters and Possible Factorizations Sec 4.1

Slides (PDF)Handouts (PDF)

5 Modulation and Polyphase Representations: Noble Identities; Block Toeplitz Matrices and Block z-transforms; Polyphase Examples Sec 3.4, 4.1-4.4

Slides (PDF)Handouts (PDF)

6 MATLAB® Wavelet Toolbox

Slides (PDF)Handouts (PDF)

HW 1 due

HW 2 out (PDF)

7 Orthogonal Filter Banks: Paraunitary Matrices; Orthogonality Condition (Condition O) in the Time Domain, Modulation Domain and Polyphase Domain Sec 5.1-5.2

Slides (PDF)Handouts (PDF)

8 Maxflat Filters: Daubechies and Meyer Formulas. Spectral Factorization Sec 5.3-5.5

Slides (PDF)Handouts(PDF)

9 Multiresolution Analysis (MRA): Requirements for MRA; Nested Spaces and Complementary Spaces; Scaling Functions and Wavelets Sec 1.5, 6.1

Slides (PDF)Handouts (PDF)

10 Refinement Equation: Interative and Recursive Solution Techniques; Infinite Product Formula; Filter Bank Approach for Computing Scaling Functions and Wavelets Sec 6.2-6.4

Slides (PDF)Handouts (PDF)

HW 2 due

HW 3 out (PDF)

11 Project Brief
12 Orthogonal Wavelet Bases: Connection to Orthogonal Filters; Orthogonality in the Frequency Domain. Biorthogonal Wavelet Bases Sec 6.2, 6.4, 6.5

Slides (PDF)Handouts (PDF)

13 Mallat Pyramid Algorithm Sec 1.6, 6.2

Slides (PDF)Handouts (PDF)

14 Accuracy of Wavelet Approximations (Condition A); Vanishing Moments; Polynomial Cancellation in Filter Banks Sec 7.1

Slides (PDF)Handouts (PDF)

15 Smoothness of Wavelet Bases: Convergence of the Cascade Algorithm (Condition E); Splines. Bases vs. Frames Sec 7.2-7.4

Slides (PDF)Handouts (PDF)

HW 3 due
16 Signal and Image Processing: Finite Length Signals; Boundary Filters and Boundary Wavelets; Wavelet Compression Algorithms Sec 8.1-8.3, 8.5, 10.1, 11.1-11.5

Slides (PDF)Handouts (PDF)

17 Guest Lecture. Physical Wavelets and their Sources: Real Physics in Complex Spacetime
18 Lifting: Ladder Structure for Filter Banks; Factorization of Polyphase Matrix into Lifting Steps; Lifting Form of Refinement Equation Sec 6.5

Slides (PDF)Handouts (PDF)

19 Wavelets and Subdivision: Nonuniform Grids; Multiresolution for Triangular Meshes; Representation and Compression of Surfaces

Slides 1 (PDF)
Slides 2 (PDF)

Handouts
1 (PDF)Handouts 2 (PDF)

20 Numerical Solution of PDEs: Galerkin Approximation; Wavelet Integrals (Projection Coefficients, Moments and Connection Coefficients); Convergence. Subdivision Wavelets for Integral Equations. Compression and Convergence Estimates Sec 11.6

Slides (PDF)Handouts (PDF)

21 M-band Wavelets: DFT Filter Banks and Cosine Modulated Filter Banks. Multiwavelets Sec 7.5, 9.1-9.4

Slides (PDF)Handouts (PDF)

22 Project Presentations
23 Project Presentations
24 Project Presentations
25 Project Presentations

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