MATHEMATICAL PRINCIPLES OF SIGNAL PROCESSING: FOURIER AND WAVELET ANALYSIS

A. FOURIER ANALYSIS IN L1 Fourier Transforms of Stable Signals / Fourier Series of Locally Stable Periodic Signals / Pointwise Convergence of Fourier Series B. SIGNAL PROCESSING Filtering / Sampling / Digital Signal Processing / Subband Coding C. FOURIER ANALYSIS IN L2 Hilbert Spaces / Complete Orthonormal Systems / Fourier Transforms of Finite Energy Signals / Fourier Series of Finite Power Periodic Signals D. WAVELET ANALYSIS The Windowed Fourier Transform / The Wavelet Transform / Wavelet Orthonormal Expansions / Construction of a MRA / Smooth Multiresolution Analysis