Lecture 
Date 
What was
covered 
Notes 
Textbook Section 
1 
Jan. 26 
Introduction: Numbers and algebraic structures 
get assignment 1 
1.1 
2 
Jan. 31 
Introduction: Functions, sequences and matrices 
 
1.2 
3 
Feb. 2 
Vector Spaces, Linear Independence, Spanning, Basis 
 
2.1 
4 
Feb. 7 
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.14 
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.21 
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.28 
Fourier series: Definition, ONB, convergence, inversion. 
Matlab Code 
3.1.3 
11 
Mar. 2 
Fourier series: Parseval and Plancherel Theorems, Inversion; Examples 
return assignment 4; get assignment 5. 
3.1.3 
12 
Mar. 7 
Continuous Fourier Transform/Fourier Integrals: Plancherel Theorem and Inversion; translation and modulation; smoothing vs decay 

3.1.3 
13 
Mar. 9 
Discrete Fourier Transforms: DFT, FFT 
return assignment 5; get assignment 6 
3.2 
14 
Mar.14 
Discrete Hartley Transform; Discrete Cosine Transforms 
university closed due to weather 
3.2 
 
Mar.14 
 
REVIEW SESSION 
5:30pm7:30pm in CSIC 4122 
 
Mar.15 
 
REVIEW SESSION 
3:00pm5:00pm in MATH 0402 
15 
Mar.16 
 
First InClass Test 
 
 
Mar.2024 
 
SPRING BREAK 
 
16 
Mar.28 
Discrete Cosine Transforms (IIV) 
 
3.2 
17 
Mar.30 
Sampling: Lagrange interpolation 
 
4.1.1, 4.1.2 
18 
Apr. 4 
Sampling: Bandlimited functions; Shannon's sampling formula 
return assignment 6; get assignment 7 
4.1.3 
19 
Apr. 6 
Signal Estimation; Measurement, noise, likelihood, MLE, unbiased estimators 
 
4.2 
20 
Apr.11 
Signal Estimation: MAP and MMSE 
return assignment 7; get assignment 8 
5.1.2,5.1.3 
21 
Apr.13 
Noise Reduction in Speech Processing using the Wiener Filter 
 
Matlab code 
22 
Apr.18 
The Continuous Wavelet Transform; Scalogram; Inversion of the CWT 
return assignment 8; get assignment 9 
5.1 
23 
Apr.20 
Example of a CWT; Multi Resolution Analysis: Spaces Vj 
 
5.1,5.2 
24 
Apr.25 
MRA (2): Spaces Wj 
return assignment 9; get assignment 10 
5.2 
25 
Apr.27 
MRA (3): Linear TimeInvariant Filters 
 
5.2 
26 
May 2 
Synthesis Filter banks: scaling functions and wavelets 
return assignment 10; get assignment 11 
5.2 
27 
May 4 
Lowpass and highpass filters. 

5.2 
 
May 4 

REVIEW SESSION 
3:30pm5:30pm in CSIC 4122 
28 
May 9 
Applications: Image analysis/synthesis. Uncertainties: Heisenberg Principle and CRLB 
return assignment 11 
4.2.2 
29 
May 11 
 
Second InClass Test 

 
May 12 
 
REVIEW SESSION 
11:00am1:00pm in CSIC 4122 
 
May 13 
 
FINAL EXAM 
8:00am10:00am in CSIC 4122 