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Wavelets, Filter Banks and Applications >> Content Detail



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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 #TOPICSREADINGSLECTURE NOTESASSIGNMENTS
1Discrete-time Filters: Convolution; Fourier Transform; Lowpass and Highpass FiltersSec 1.1-1.4, 2.1

Slides (PDF)Handouts (PDF)

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

Slides (PDF)Handouts (PDF)

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

Slides (PDF)Handouts (PDF)

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

Slides (PDF)Handouts (PDF)

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

Slides (PDF)Handouts (PDF)

6MATLAB® Wavelet Toolbox

Slides (PDF)Handouts (PDF)

HW 1 due

HW 2 out (PDF)

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

Slides (PDF)Handouts (PDF)

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

Slides (PDF)Handouts(PDF)

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

Slides (PDF)Handouts (PDF)

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

Slides (PDF)Handouts (PDF)

HW 2 due

HW 3 out (PDF)

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

Slides (PDF)Handouts (PDF)

13Mallat Pyramid AlgorithmSec 1.6, 6.2

Slides (PDF)Handouts (PDF)

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

Slides (PDF)Handouts (PDF)

15Smoothness 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
16Signal and Image Processing: Finite Length Signals; Boundary Filters and Boundary Wavelets; Wavelet Compression AlgorithmsSec 8.1-8.3, 8.5, 10.1, 11.1-11.5

Slides (PDF)Handouts (PDF)

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

Slides (PDF)Handouts (PDF)

19Wavelets 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)

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

Slides (PDF)Handouts (PDF)

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

Slides (PDF)Handouts (PDF)

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




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