Time-Varying Systems and Computations WS 2011/12
36 Examination Topics
1 Linear Algebra
1.1 Solving Linear Systems of Equations
1.2 Linear Least Squares Problem
1.3 QR-Factorization, Normal Equation and Cholesky Factorization
1.4 Singular Value Decomposition, Matrix Approximation and Pseudo-Inverse
1.5 Projections, Householder Transformation, Jacobi Rotations, Elimination
1.6 Linear Maps and the 4 Fundamental Subspaces of a Matrix
2 Time Invariant Systems
2.1 Linear, Cyclic and Fast Convolution
2.2 Eigenvalue Decomposition of a Circulant Matrix and DFT
2.3 State-Space Representation and Transfer Functions
2.4 Stable Inversion of Transfer Function, Bounded Inversion of Toeplitz Matrices
2.5 Signal Flow Diagrams for State-Space Systems and Impulse Response
2.6 Causality, Linearity and Time-Invariance
3 Time-Varying Systems
3.1 Concept of Efficient Matrix Computations in State-Space
3.2 Matrices Requiring Time-Varying System Theory, Limitations of Fourier Methods
3.3 Shift-Operator, Diagonal Matrices and Diagonal Representations
3.4 State-Transformation, Transfer Functions and Impulse Response
3.5 System Model for Time-Varying State-Space System
3.6 Bounded and causal inversion of
4 Realization Theory
4.1 Toeplitz and Hankel Operators associated with Time-Varying Systems
4.2 From State-Space Representation to Toeplitz Operator
4.3 Observability and Controllability Matrices
4.4 Normal Forms for Realizations, Gramian Matrices
4.5 Shift-Invariance Property and Minimal Realizations
4.6 Factorization of Hankel Matrices and Minimal Dimension of State-space
5 Lossless Systems and Computations
5.1 Addition, Multiplication and Inversion of Matrices in State-Space
5.2 Semi-Separable Matrix Structure and Anti-causal Systems
5.3 Hankel Matrices for Anti-causal Systems and Backward State-space Equations
5.4 Lossless Bounded Real Lemma
5.5 QL Factorization of a matrix T in State-Space
5.6 Matrix Inversion via QL Factorization
6 Applications and Architectures
6.1 TBD after Poster Session
6.2 TBD after Poster Session
6.3 TBD after Poster Session
6.4 TBD after Poster Session
6.5 TBD after Poster Session
6.6 TBD after Poster Session