mexihat function

Mexicat Hat

Generate a Mexican Hat (Ricker) wavelet sampled on a regular grid.

mexihat(lb = -5, ub = 5, n = 1000)

Arguments

• lb, ub: Lower and upper bounds of the interval to evaluate the wavelet on. Default: -5 to 5.
• n: Number of points on the grid between lb and ub (length of the wavelet). Default: 1000.

Returns

A list containing 2 variables; x, the grid on which the complex Mexican Hat wavelet was evaluated, and psi ($\Psi$), the evaluated wavelet on the grid x.

Details

The Mexican Hat or Ricker wavelet is the negative normalized 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. The Ricker wavelet is frequently employed to model seismic data, and as a broad spectrum source term in computational electrodynamics. It is usually only referred to as the Mexican hat wavelet in the Americas, due to taking the shape of a sombrero when used as a 2D image processing kernel. It is also known as the Marr wavelet (source: Wikipedia)

Examples

mh <- mexihat(-5, 5, 1000)
plot(mh$x, mh$psi, type="l", main = "Mexican Hat Wavelet",
     xlab = "", ylab = "")

Author(s)

Sylvain Pelissier, sylvain.pelissier@gmail.com .

Conversion to R by Geert van Boxtel, G.J.M.vanBoxtel@gmail.com .