Lecture Notes and Handouts

These handouts are in .pdf format.  These can be viewed with Adobe Acrobat Reader (freeware available off the web).

Please let me know if you notice any typos or mistakes in these... even if it is just a grammar mistake or a misspelled word.  I will gladly correct any mistakes that you find.

The sections listed are the corresponding sections from the textbook (Frazier).  I haven't covered all of the results as we are not going to need them during this course.

Lecture 1 -- Complex Numbers (9/10/01) -- Sections 1.1, 1.2 (corrections made 10/28/01)
Lecture 2 -- Vector Spaces and Bases (9/12/01, 9/17/01) -- Sections 1.3, 1.4
Lecture 3 -- Inner Product Spaces and Orthonormal Bases (9/17/01) -- Section 1.6 (corrections made 9/24/01)
Lecture 4 -- The Discrete Fourier Transform (9/18/01) -- Section 2.1 (corrections made 10/10/01)
Lecture 5 -- The Fourier Basis and the Fourier Inversion Formula (9/19/01) -- Section 2.1 (corrections made 10/03/01)
Lecture 6 -- Interpreting the Fourier Transform and Some Basic Properties (9/24/01) -- Sections 2.1, 2.2 (corrections made 10/28/01)
Lecture 7 -- The Fast Fourier Transform  (9/26/01) -- Section 2.3
Lecture 8 -- Sequences, Series, and Hilbert Spaces (10/01/01) -- Sections 4.1, 4.2
Lecture 9 -- The Fourier Series (10/02/01) -- Section 4.3 (corrections made 10/08/01)
Lecture 10 -- The Fourier Transform on R (10/08/01) -- Section 5.2 (corrections made 10/08/01)
Lecture 11 -- Shannon's Sampling Theorem (10/09/01) -- Section 5.3 (Exercises)

Lecture 12 -- The Orthogonal Decomposition Theorem (10/17/01) -- Section 3.2 (corrections made 10/28/01)
Lecture 13 -- What is a Wavelet? (10/22/01) -- Section 3.1
Lecture 14 -- Haar Wavelets (10/22/01) -- Section 3.3 (corrections made 11/26/01)
Lecture 15 -- First Stage Wavelet Bases for Zn (10/23/01) -- Section 3.1 (corrections made 11/4/01)
Lecture 16 -- The Iteration Step for Wavelets on Zn (10/29/01) -- Section 3.2 (corrections made 11/26/01)
Lecture 17 -- The pth Stage Wavelet Basis for Zn (10/30/01) -- Section 3.2 (corrections made 11/4/01)
Lecture 18 -- Alternate Constructions of the pth Stage Wavelet Basis (10/31/01) -- (corrections made 11/28/01)
Lecture 19 -- Daubechies Wavelets (11/7/01) -- Section 3.3

Lecture 20 -- The Continuous Wavelet Transform (11/12/01) -- Section 5.3 (corrections made 12/9/01)
Lecture 21 -- The Discrete Wavelet Transform and Multiresolution (11/13/01) -- Section 5.3 (corrections made 12/9/01)
Lecture 22 -- Where are the Wavelets? (Part I)  (11/14/01) -- Section 5.3
Lecture 23 -- Where are the Wavelets? (Part II) (11/19/01) -- Section 5.3 (corrections made 11/28/01)
Lecture 24 -- Fourier Constructions (11/20/01) -- Section 5.4
Lecture 25 -- Construction of Scaling Sequences (11/26/01) -- Section 5.4, 5.5 (updated 11/28/01)