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.