Complex Mexican hat wavelet
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. for applications requiring high temporal precision time-frequency analysis.
