Lecture 
Date 
What was
covered 
Notes 
Textbook Section 
1 
Jan. 26 
Introduction 
canceled due to snow 
1.1 
2 
Jan. 28 
Introduction: Numbers and algebraic structures 
get assignment 1 
1.1 
3 
Feb. 2 
Introduction: Functions, sequences and matrices 
 
1.2 
4 
Feb. 4 
Vector Spaces, Linear Independence, Spanning, Basis 
return assignment 1; get assignment 2 
2.1 
5 
Feb. 9 
Vector spaces: Basis theorem; Norms and Banach space 
 
2.1 
6 
Feb.11 
Scalar products and Hilbert spaces; CauchySchwarz inequality; Schauder basis; Orthonormal basis;GrammSchmidt orthonormalization; biorthogonal basis. 
 
2.2 
7 
Feb.16 
Subspaces, Linear transformations, Matrix representation, Matrix Algebra 
return assignment 2; get assignment 3. 
2.2 
8 
Feb.18 
The adjoint operator; orthogonal projections 
 
2.2 
9 
Feb.23 
Projections onto range and kernel of linear operators; direct sums and orthogonal decompositions 
return assignment 3; get assignment 4 
2.2 
10 
Feb.25 
Fourier series: Definition, ONB, convergence, inversion. 
Matlab Code 
3.1.3 
11 
Mar. 1 
Fourier transform: Definition, Plancherel Theorem, RiemannLebesgue Lemma, Inversion 
return assignment 4; get assignment 5. 
3.1.3 
12 
Mar. 3 
Continuous Fourier Transform: Windowing; smoothing vs decay 

3.2 
13 
Mar. 8 
Discrete Fourier Transforms: DFT, FFT 
return assignment 5 
3.2 
 
Mar. 9 
REVIEW SESSION 
 
Wed. Mar. 9, 3:30pm5:00pm in CSIC 4122 
14 
Mar.10 
 
First InClass Test 
 
15 
Mar. 22 
Discrete Hartley Transform; Discrete Cosine Transforms 
get assignment 6 
3.2 
16 
Mar.24 
Sampling: Lagrange interpolation 
 
4.1.1, 4.1.2 
17 
Mar.29 
Sampling: Bandlimited functions; Shannon's sampling formula 
return assignment 6; get assignment 7 
4.1.3 
18 
Mar.31 
Signal Estimation; Measurement, noise, likelihood, MLE, unbiased estimators 
 
4.2 
19 
Apr. 5 
Signal Estimation: MAP and MMSE 
return assignment 7; get assignment 8 
5.1.2,5.1.3 
20 
Apr. 7 
The Continuous Wavelet Transform; Scalogram; Inversion of the CWT 
 
5.2.1 
21 
Apr.12 
Discrete Wavelet Transform: frames to basis; MRA (1) 
return assignment 8; get assignment 9 
5.2.1, 5.2.2, 5.2.3 
22 
Apr.14 
MRA (2): Spaces Vj 
 
5.2.3 
23 
Apr.19 
MRA (3): Spaces Wj 
return assignment 9; get assignment 10 
5.3 
24 
Apr.21 
MRA (4): Linear TimeInvariant Filters 
 

25 
Apr.26 
Synthesis Filter banks: scaling functions and wavelets 
return assignment 10; get assignment 11 

26 
Apr.28 
Applications: Image analysis/synthesis 


27 
May. 3 
Application: Interplay between statistical signal processing and linear transforms 
return assignment 11 

 
May. 4 
REVIEW SESSION 
 
Wed. May 4, 3:00pm4:30pm in CSIC 4122 
28 
May 5 
 
Second InClass Test 

29 
May.10 
Uncertainty Inequalities: Heisenberg principle; CRLB 
Last Class 
4.2.2 
 
May.10 
REVIEW SESSION 
 
Tues. May 10, 2:00pm4:00pm in MATH B0431 
 
May. 12 
FINAL EXAM 
FINAL EXAM 
8:00am10:00am in CSIC 4122 