EE 6350: Signal Theory

Fall 2007

Instructor	Aria Nosratinia, ECSN 4.208 Tel: 972-883-2894
Time	Mon-Wed. 5:30-6:45pm
Place	ECSS 2.312
Office Hours	3:30-4:30pm Mon. & Wed.
Textbook	Moon and Stirling: Mathematical Methods and Algorithms for Signal Processing, Prentice-Hall
TA	Negar Bazargani (negar.bazargani@student.utdallas.edu) Office hours Tue-Thu 5-6pm, ECSN 4.206

Course Notes

(0) Course Logistics
(1) Linear Algebra Review
(2) Signal Spaces
(3) Approximation in Vector Spaces
(4) Linear Operators and Inverse Problems
(5) Matrix Decompositions

This course is designed to prepare the students for advanced studies and research in (digital) signal processing and communications. It explores the fundamentals of signal representation and approximation, with an emphasis on minimum mean square theory and Hilbert space approximation. The course starts with a basic overview of matrix and vector analysis, followed by a coverage of least squares (LS) solutions, where the power and breadth of the orthogonality principle and its applications in signal processing are emphasized. Minimum-norm and MNLS solutions, psuedo-inverses, eigen-value and singluar-value decompositions are treated in detail. Time permitting, additional advanced topics will also be visited.

Signal Spaces
- Vector spaces
- Norms
- Inner products and orthogonality
- Linear transformations
- Projections
Representation and Approximation in Vector Spaces
- The orthogonality principle
- Matrix representation of LS problems
- Applications
Linear Operators and Matrix Inverses
- Linear Operators
- Operator Norms
- Adjoint Operators
- Four fundamental subspaces
- Matrix inverses, min. norm and least squares solutions
- Psuedo-inverses
Matrix Factorizations
- LU factorization
- Cholesky factorization
- QR factorization
Eigen-Decompositions
- Eigenvalues and eigenvectors
- Diagonalization
- Invariant subspaces
- Quadratic forms
- Applications
Singular Value Decomposition
- The Eckart-Young Theorem
- SVD approximation
- Relation with psuedo-inverses
Advanced Topics
- Extension to infinite dimensions
- Hilbert spaces
- The Hilbert space of zero-mean random variables
- MMSE approximation of random variables
- Generalized Fourier decompositions
- Energy preserving transformations, the generalized Parseval equality

Aria Nosratinia

Last modified: August 2007

EE 6350: Signal Theory

Fall 2007

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