Continuous Wavelet Transform

Definition

The continuous wavelet transform transforms continuous time domain function $f(t)$ into time and scale domain function $W(a,b)$. $W(a,b)=\frac{1}{\sqrt{a}}{\int }_{-\infty }^{\infty }f(t)\overline{\psi }\left(\frac{t-b}{a}\right)dt$ where $\psi (t)$ is a mother wavelet or wavelet function, $a\in {\mathbb{R}}^{+}$ is a scale parameter, $b\in \mathbb{R}$ is a translational parameter.

Facts

Unlike the Fourier Transform, wavelet transform provides good localization in both time and frequency domains.