Lecture 
Date 
What was
covered 
Notes 
Textbook Section 
1 
Sept. 3 
Introduction; Continuity and Differentiability 
get assignment 1 
 
2 
Sept.
5 
Integrability (L1, L2, Lp spaces); Vector Spaces 
 
 
3 
Sept. 10 
Orthonormal Bases; Linear Independence, Spanning; Orthogonal Projections 
 
 
4 
Sept.
12 
Fourier series (I): Definition and examples 
turn in assignment 1; get assignment 2. Matlab Code 
1.3 
5 
Sept.
17 
Fourier series (II): L^2 theory 
turn in assignment 2 
1.3 
6 
Sept.
19 
Fourier series (III): pointwise convergence 
get assignment 3 
1.5 
7 
Sept.
24 
Fourier series: Gibbs phenomenon; meansquare and pointwise approximation error estimates 
turn in assignment 3; get assignment 4. Matlab Code 
1.5 
8 
Sept. 26.

Fourier Series: Heat Equation; Other Examples 
 
1.1, 3.1 
 
Sept. 30 
REVIEW SESSION
in Kim Jeong Building: KEB 1200 
turn in assignment 4 before Review Session;
57pm KEB 1200 
 
9 
Oct. 1 
MIDTERM 1 
CSIC 4122 
Chapters 1, (selected topics of) 4, Chapter 9, sect.9.3 (pages 548553) 
10 
Oct.
3 
Fourier transform: Definition; Examples 

3.1 
11 
Oct.
8 
Plancherel Formula; Poisson Summation Formula 
get assignment 5 
3.2, 1.4 (3337) 
12 
Oct.
10 
Rules for computing FT (I) 

3.2 
13 
Oct.
15 
Rules for computing FT (II); smoothnes vs. decay; sinecosine transforms 
turn in assignment 5; get assignment 6; EGR 1110 
3.3(153),4.2(193), 
14 
Oct.17 
convolutions; integral equations 
EGR 1110; 
Problem 1.3; 2.1,2.2, 2.3 
15 
Oct. 22 
Sampling of bandlimited signals; Shannon formula; reconstruction error (I) 
turn in assignment 6; get assignment 7 
8.1, 8.2, 8.4 
16 
Oct. 24 
Oversampling and reconstruction error (II) 

8.2, 8.4 
17 
Oct.
29 
convolutions  discrete signals & Fourier series 
turn in assignment 7;get assignment 8 
1.2 (1619), 2.3 (105106) , 2.4 
 
Oct. 29 
REVIEW SESSION 
MATH 0304 
3:00pm  5:00pm 
18 
Oct.
31 
MIDTERM 2 
CSIC 4122 

19 
Nov. 5 
Windowed Fourier transform  analysis/synthesis and L2 
turn in assignment 8; get assignment 9 
11.2, 11.3, 11.4 
20 
Nov.
7 
wFT  Time and Frequency separation / Instantaneous Frequency (1) 
spectrogram code 
11.2, 11.3, 11.4 
21 
Nov.
12 
ShortTime Fourier Transform  discrete time 
turn inassignment 9; get assignment 10 
11.2, 11.3, 11.4 
22 
Nov.
14 
Instantaneous Frequency (2); Time and Bandlimited functions 

11.4 , 12.4 (pg. 761) 
23 
Nov.
19 
Uncertainty Inequality; Continuous Wavelet Transform 
turn in assignment 10; get assignment 11 
11.4 , 12.4 (pg. 761) 
24 
Nov.
21 
cWT  Analysis and Synthesis; Examples 

10.1 
25 
Nov.
26 
Wavelet Bases: Haar Basis (1) 

10.1 
26 
Nov.
28 
THANKSGIVING BREAK 

No Class 
27 
Dec.3 
Haar Basis (2) 
turn in assignment 11; get assignment 12 
10.1 
28 
Dec.5 
Haar Basis & MRA 

10.2 
29 
Dec.10 
MRA 

10.2, 10.3 
30 
Dec.12 
MRA 
turn in assignment 12; Last Class 
10.3 
 
Dec.12 
REVIEW SESSION 
MATH 0401 
2:00pm  4:30pm 
 
Dec.16 
FINAL EXAM 
CSIC 4122 
Comprehensive 