Applied & Computational Harmonic Analysis: Comments, Handouts, and References Page (Winter 2014)

Course: MAT 271
CRN: 84077
Title: Applied & Computational Harmonic Analysis
Class: TR 1:40pm-3:00pm,  Physics 140

Instructor: Naoki Saito 
Office: 2142 MSB 
Phone: 754-2121
Office Hours: TR 3:10pm-4:00pm, or by appointment

The following references are useful and contains much more details of the topics covered or referred to in my lectures. I strongly encourage you to take a look at some of them.

Lecture 1: Overture and Motivation; What is a Signal?
Lecture 2: Basics of the Fourier Transforms
Lecture 3: Uncertainty Principles
Lecture 4: Bandlimited Functions and Sampling Theorems; Periodization vs Sampling
Lecture 5: Basic Theory of Fourier Series; Smoothness of Functions and Decay Rate of the Fourier Coefficients
Lecture 6: Functions of Bounded Variations; the Decay Rate of the Fourier Coefficients II; Fourier Series on Intervals
Lecture 7: Discrete Fourier Transform
Lecture 8: Fast Fourier Transform (FFT)
Lecture 9: From the Sturm-Liouville Theory to Discrete Cosine and Sine Transforms (DCT/DST)
Lecture 10: Karhunen-Loève Transform (KLT)
Lecture 11: Time-Frequency Analysis and Synthesis; Windowed (or Short-Time) Fourier Transform

Lecture 12: Introductory Frame Theory; The Balian-Low Theorem

Lecture 13: Continuous Wavelet Transform

Lecture 14: Continuous Wavelet Transform II: Analytic Wavelets

Lecture 15: Discrete Wavelet Transforms; Multiresolution Approximation; Scaling Functions

Lecture 16: Conjugate Mirror Filters; Mother Wavelets; Orthonormal Wavelet Basis

Lecture 17: Vanishing Moments; Support Size; Regularity; and Daubechies's Compactly Supported Wavelets

Lecture 18: Fast Wavelet Transforms; Various Extensions

Lecture 19: A Library of Othonormal Bases and Adapted Signal Analysis

Lecture 20: Multiscale Basis Dicionarites on Graphs and Networks