Continuous wavelet transform

In mathematics, a continuous wavelet transform (CWT) is used to divide a continuous-time function into wavelets. Unlike Fourier transform, the continuous wavelet transform possesses the ability to construct a time-frequency representation of a signal that offers very good time and frequency localization. The continuous wavelet transform of a function ${\displaystyle x(t)}$ at a scale (a>0) ${\displaystyle a\in \mathbb {R^{+*}} }$ and translational value ${\displaystyle b\in \mathbb {R} }$ is expressed by the following integral

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