Routines (alphabetical) > Routines: W > 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[–(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 ; 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 simply 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

## See Also

WV_CWT, WV_FN_GAUSSIAN, WV_FN_PAUL