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
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
See Also
WV_CWT, WV_FN_MORLET, WV_FN_PAUL