Continuous wavelet transform

In mathematics, the continuous wavelet transform (CWT) is a formal (i.e., non-numerical) tool that provides an overcomplete representation of a signal by letting the translation and scale parameter of the wavelets vary continuously. == Definition == The continuous wavelet transform of a function x ( t ) {\displaystyle x(t)} at a scale a ∈ R + ∗ {\displaystyle a\in \mathbb {R^{+*}} } and translational value b ∈ R {\displaystyle b\in \mathbb {R} } is expressed by the following integral X w ( a , b ) = 1 | a | 1 / 2 ∫ − ∞ ∞ x ( t ) ψ ¯ ( t − b a ) d t {\displaystyle X_{w}(a,b)={\frac {1}{|a|^{1/2}}}\int _{-\infty }^{\infty }x(t){\overline {\psi }}\left({\frac {t-b}{a}}\right)\,\mathrm {d} t} where ψ ( t ) {\displaystyle \psi (t)} is a continuous function in both the time domain and the frequency domain called the mother wavelet and the overline represents operation of complex conjugate.

Source: Wikipedia — Continuous wavelet transform (CC BY-SA 4.0)