**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