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### WV_FN_MORLET

WV_FN_MORLET

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[–(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 ; pick a nice number of points`
`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

 5.4 Introduced