Ricker wavelet
In mathematics and numerical analysis, the Ricker wavelet, Mexican hat wavelet, or Marr wavelet (for David Marr) ψ ( t ) = 2 3 σ π 1 / 4 ( 1 − ( t σ ) 2 ) e − t 2 2 σ 2 {\displaystyle \psi (t)={\frac {2}{{\sqrt {3\sigma }}\pi ^{1/4}}}\left(1-\left({\frac {t}{\sigma }}\right)^{2}\right)e^{-{\frac {t^{2}}{2\sigma ^{2}}}}} is the negative normalized ( ∫ R ψ 2 = 1 ) {\displaystyle \left(\int _{\mathbb {R} }\psi ^{2}=1\right)} second derivative of a Gaussian function, i.e., up to scale and normalization, the second Hermite function. It is a special case of the family of continuous wavelets (wavelets used in a continuous wavelet transform) known as Hermitian wavelets.