Wavelet transform

In mathematics, a wavelet series is a representation of a square-integrable (real- or complex-valued) function by a certain orthonormal series generated by a wavelet. Nowadays, wavelet transformation is one of the most popular time-frequency-transformations. This article provides a formal, mathematical definition of an orthonormal wavelet and of the integral wavelet transform.

A function ${\displaystyle \scriptstyle \psi \,\in \,L^{2}(\mathbb {R} )}$ is called an orthonormal wavelet if it can be used to define a Hilbert basis, that is a complete orthonormal system, for the Hilbert space ${\displaystyle \scriptstyle L^{2}\left(\mathbb {R} \right)}$ of square integrable functions.

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