ECE 6250, Fall 2016, Notes

Signal Discretization using Basis Decompositions
Notes 1, the Shannon-Nyquist sampling theorem
Notes 2, introduction to basis expansions
Notes 3, linear signal spaces
Notes 4, norms and inner products
Notes 5, linear approximation
Notes 6, orthobases
Notes 7, Parseval’s theorem and the Gram-Schmidt algorithm
Notes 8, cosine transforms, jpeg image compression
Notes 9, the lapped orthogonal transform
Notes 10, the Haar wavelet transform
Notes 11, orthonormal wavelet bases
Notes 12, non-orthogonal Riesz bases
Notes 13, B-splines

Linear Inverse Problems and Least-Squares Signal Processing
Notes 14, discretizing inverse problems
Notes 15, solving systems of symmetric equations
Notes 16, the SVD and the least-squares problem
Notes 17, stable least-squares
Notes 18, weighted least-squares and the BLUE

Computing the Solution to Least-Squares Problems
Notes 19, matrix factorization
Notes 20, Toeplitz matrices
Notes 21, iterative methods: steepest descent and conjugate gradients
Notes 22, recursive least-squares
Notes 23, the Kalman filter
Notes 24, adaptive filtering

Matrix Approximation using Least-Squares
Notes 25, the SVD and matrix approximation, total least-squares, PCA

Beyond Least-Squares
Notes 26, norm approximation problems