DOG: Create a Derivative Of Gaussian Wavelet

In ArcadeAntics/wavelet.analysis: Performing Wavelet Analysis

Description

A DOG wavelet is defined as

Ψ(t) = D^m(exp(-t^2/2))

the m-th derivative of a standard Gaussian function (a Gaussian function with mean 0 and variance 1)

Usage

DOG(m = 2L)

Arguments

m	positive integer; the order / / derivative number of the DOG wavelet

Details

A DOG wavelet is a real-valued wavelet, and as such is better for isolating peaks or discontinuities in a signal

A DOG wavelet of order 2 is also called the Mexican hat / / Ricker wavelet.

Value

A function of class c("DOG", "Wavelet", "function")

References

Torrence and Compo 1998

Examples

plot(DOG(), -5, 5, n = 1001,
    xlab = "t", ylab = "\u03a8(t)", main = "Mexican hat wavelet")


plot(DOG(6), -5, 5, n = 1001,
    xlab = "t", ylab = "\u03a8(t)", main = "DOG wavelet, order 6")

ArcadeAntics/wavelet.analysis documentation built on Jan. 19, 2021, 12:32 a.m.