gsignal (version 0.3-7)

mexihat: Mexicat Hat

Description

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

Usage

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

Value

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.

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.

Author

Sylvain Pelissier, .
Conversion to R by Geert van Boxtel, .

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 = "")