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WV_FN_GAUSSIAN

WV_FN_GAUSSIAN

The WV_FN_GAUSSIAN function constructs wavelet coefficients for the Gaussian wavelet function. In real space, the Gaussian wavelet function is proportional to the m-th order derivative of a Gaussian, exp(–x2/2). The Gaussian second derivative, (x2–1) exp(–x2/2), is often referred to as the Marr wavelet.

Examples

Plot the Gaussian wavelet function at scale=20:

n = 1000 ; pick a nice number of points
info = WV_FN_GAUSSIAN( 2, 20, n, /SPATIAL, \$
WAVELET=wavelet)
plot, wavelet

Now plot the same wavelet in Fourier space:

info = WV_FN_GAUSSIAN( 2, 20, n, \$
FREQUENCY=frequency, WAVELET=wave_fourier)
plot, frequency, wave_fourier, \$
xrange=[-0.2,0.2], thick=2

Syntax

Result = WV_FN_GAUSSIAN( [Order] [, Scale, N]
[, /DOUBLE] [, FREQUENCY=variable] [, /SPATIAL] [, WAVELET=variable])

The returned value of this function is an anonymous structure of information about the particular wavelet.

 Tag Type Definition FAMILY STRING ‘Gaussian’ ORDER_NAME STRING ‘Derivative’ ORDER_RANGE DBLARR(3) Valid orders [first, last, default] ORDER DOUBLE The chosen Order DISCRETE INT 0 [0=continuous, 1=discrete] ORTHOGONAL INT 0 [0=nonorthogonal, 1=orthogonal] SYMMETRIC INT 1 [0=asymmetric, 1=symm.] SUPPORT DOUBLE Infinity [Compact support width] MOMENTS INT 1 [Number of vanishing moments] REGULARITY DOUBLE Infinity [Number of continuous derivatives] E_FOLDING DOUBLE SQRT(2) [Autocorrelation e-fold distance] FOURIER_PERIOD DOUBLE Ratio of Fourier wavelength to scale

Arguments

Order

A scalar that specifies the non-dimensional order parameter for the wavelet. The default is 2.

Scale

A scalar that specifies the scale at which to construct the wavelet function.

N

An integer that specifies the number of points in the wavelet function. For Fourier space (SPATIAL=0), the frequencies are constructed following the FFT convention:

• For N even: 0, 1/N, 2/N, ..., (N–2)/(2N), 1/2, –(N–2)/(2N), ..., –1/N.
• For N odd: 0, 1/N, 2/N, ..., (N–1)/(2N), –(N–1)/(2N), ..., –1/N.

For real space (/SPATIAL), the spatial coordinates are –(N–1)/2...(N–1)/2.

Note: If none of the above arguments are present then the function will return the Result structure using the default Order.

Keywords

DOUBLE

Set this keyword to force the computation to be done in double-precision arithmetic.

FREQUENCY

Set this keyword to a named variable in which to return the frequency array used to construct the wavelet. This variable will be undefined if SPATIAL is set.

SPATIAL

Set this keyword to return the wavelet function in real space. The default is to return the wavelet function in Fourier space.

WAVELET

Set this keyword to a named variable in which to return the wavelet function.

Reference

Torrence and Compo, 1998: A Practical Guide to Wavelet Analysis. Bull. Amer. Meteor. Soc., 79, 61–78.

Version History

 5.4 Introduced