Complex Mexican hat wavelet

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In applied mathematics, the complex Mexican hat wavelet is a low-oscillation, complex-valued, wavelet for the continuous wavelet transform. This wavelet is formulated in terms of its Fourier transform as the Hilbert analytic signal of the conventional Mexican hat wavelet:

Temporally, this wavelet can be expressed in terms of the error function, as:

This wavelet has asymptotic temporal decay in , dominated by the discontinuity of the second derivative of at .

This wavelet was proposed in 2002 by Addison et al.[1] for applications requiring high temporal precision time-frequency analysis.