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In Mathematics and Numerical Analysis , the Mexican hat wavelet is the normalized, second Derivative of a Gaussian Function . It is a special case of the more general family of continuous wavelets (wavelets used in a Continuous Wavelet Transform ) known as Hermitian Wavelet s.

:\psi (t) = \left( {2 \over {\sqrt 3 }}\pi^{- {1 \over 4} } ight) \left( 1-t^2 ight)e^{ - {t^2} \over 2 }

The hyperdimensional generalization of this wavelet is called the '' Laplacian of Gaussian'' function. In practice, this wavelet is often approximated by the '' Difference Of Gaussians '' function, as it is easier to compute.