Digital Biomedical Signal Processing: Advanced Topics / Luca T. Mainardi
2008
Z jcðtÞj2dtoþN (8) Therefore, continuous wavelets c(t) have zero-mean and finite energy. In practice, they are oscillating around the t axis and vanishing with time (see Fig. 1a). In general, as CðoÞ ! 0 when, o-N wavelets have a band pass-like spectrum. Other important properties include regularity, null vanishing moments, orthogonality, and finite support.[5] Some analogies between FT and CWT exist: they are linear operators, and both transforms can be viewed as a projection of a function into a different domain. For the FT, this new domain contains basis functions that are sines and cosines. For the wavelet transform, this new domain contains more complicated basis functions called wavelets. The main difference lies in the fact that wavelets are usually localized in time, whereas complex exponentials are not (see Fig. 1a).