# Wavelet central frequency

What is the definition of the central frequency of a Wavelet and the bandwidth of a Wavelet? How do they affect the resultant waveform of the wavelet?

Thanks.

• it looks like, in the case of the Morlet wavelet there is an explicit answer to your question. (and it is not exactly what i would expect, but i need to read it a little more.) i don't know of a general definition of "central frequency" or "bandwidth" for every arbitrary wavelet definition. – robert bristow-johnson Apr 30 '18 at 2:59

It's not formally defined, however I've seen $$\int_{-\infty}^\infty \omega |\Psi(\omega)|^2 d\omega$$ be used in the literature (i.e. the centre of mass of $$|\Psi(\omega)|^2$$), where $$\Psi$$ is the Fourier transform of the wavelet $$\psi$$.