The WV_FN_MORLET function constructs wavelet coefficients for the Morlet wavelet function. In real space, the Morlet wavelet function consists of a complex exponential modulated by a Gaussian envelope: π–1/4s–1/2 exp[i k x / s] exp[–(x / s)2/2], where s is the wavelet scale, k is a non-dimensional parameter, and x is the position.
Examples
Plot the Morlet wavelet function at scale=100:
n = 1000
info = WV_FN_MORLET( 6, 100, n, /SPATIAL, $
WAVELET=wavelet)
plot, float(wavelet), THICK=2
oplot, imaginary(wavelet)
Now plot the same wavelet in Fourier space:
info = WV_FN_MORLET( 6, 100, n, $
FREQUENCY=frequency, WAVELET=wave_fourier)
plot, frequency, wave_fourier, $
xrange=[-0.2,0.2], thick=2
Syntax
Result = WV_FN_MORLET( [Order] [, Scale, N] [, /DOUBLE] [, FREQUENCY=variable] [, /SPATIAL] [, WAVELET=variable])
Return Value
The returned value of this function is an anonymous structure of information about the particular wavelet.
|
Tag |
Type |
Definition |
|
FAMILY |
STRING |
‘Morlet’ |
|
ORDER_NAME |
STRING |
‘Parameter’ |
|
ORDER_RANGE |
DBLARR(3) |
[3, 24, 6] 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 6.
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_GAUSSIAN, WV_FN_PAUL