Introduction to time frequency analysis; the how, what and why about wavelets.;Short-time Fourier transform, Wigner-Ville transform.;Continuous time wavelet transform, Discrete wavelet transform, tiling of the time-frequency plane and wavepacket analysis.;Construction of wavelets. Multiresolution analysis. Introduction to frames and biorthogonal wavelets.;Multirate signal processing and filter bank theory.;Application of wavelet theory to signal denoising, image and video compression, multi-tone digital communication, transient detection.