**Texts:** *An introduction to wavelets through linear algebra*,
by M. Frazier

* A wavelet tour of signal processing* by S. Mallat

**SUGGESTED PROBLEMS FROM CHAPTERS 2 & 3 IN FRAZIERS's BOOK: **

Computational problems:

Section 2.1: 2.1.6, 2.1.7.

Section 2.2: 2.2.7, 2.2.9.

Section 3.1-3.3: 3.1.2-3.3.1 (Haar basis), 3.1.8-3.3.2 (Shannon basis), 3.3.3 (real Shannon wavelets, see example 3.11) .

2-Dimensional sequence:

Section 2.1: 2.1.15, 2.1.16, 2.1.17, 2.1.18, 2.1.19.

Section 2.2: 2.2.18, 2.2.19, 2.2.20.

Section 2.3: 2.3.10.

Section 3.1: 3.1.12, 3.1.14

Section 3.2: 3.2.13, 3.2.14

Counting problems:

Section 3.2: 3.2.4, 3.2.12

Characterization of finite dim filters/wavelets

Section 3.1: 3.1.6 (parameterization of unitary matrices)

Section 3.2: 3.2.9 (all finite dim. wavelet basis come from wavelet filters), 3.2.10 ( every vector in dimension 2^n and with length 1 is a wavelet!).

Return to: Department of Mathematics and Statistics, University of New Mexico

Last updated: October 12, 2001