4. Orthonormal Wavelets
Charles K. Chui · Society for Industrial and Applied Mathematics eBooks · 1997
For signal analysis, a wavelet ψ(t) is considered to be a bandpass window function that stops at least the zero frequency; namely,∫−∞∞ψ(t)ⅆt=ψ^(0)=0.This property enables the integral wavelet transform (IWT), or continuous wavelet transform (CWT), with ψ(t) as the analyzing wavelet, to annihilate the flat (i.e., near-constant) segments of the analog signal and thus provide a better understanding of its details. If ψ(t) has vanishing moments of a higher order, meaning that∫−∞∞tkψ(t)dt=0,k=0,…,m−1,for some integer m≥2 , then even the “smooth polynomial” segments are annihilated, and the IWT can better reveal the details of the signal on each octave band by considering different scales a (see section 6.5 in Chapter 6).