Adv. Digital Signal Processing - Multirate and wavelets

The subject of wavelets has received considerable attention over the last twenty years, with contributions coming from researchers in electrical engineering, mathematics and physics. The word "wavelet" refers to a little wave, and implies functions that are reasonably localized both in the Time Domain and in the Fourier Domain. The idea stems from the limitation posed by the Uncertainty Principle, which puts a limit on simultaneous localization in the time and frequency domains. As in the case of the Uncertainty Principle of Physics, the implications are seen more when one would like to make a microscopic analysis of signals. In a number of signal processing situations, one does indeed need to look at local features: in fact, the requirement of simultaneous localization is far more widespread than often perceived. For example, there are many situations in audio, image and video where, for the purpose of analysis, one very often wishes to focus one's attention on a specific time/ space range and frequency range simultaneously.