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### WV_CWT

WV_CWT

The WV_CWT function returns the one-dimensional continuous wavelet transform of the input array. The transform is done using a user-inputted wavelet function.

## Example

`; Assume we have monthly random data.`
`n = 500`
`dt = 1d/12  ; time sampling`
`seed = 999`
`data = RANDOMN(seed, n)`
`time = 1960 + dt*FINDGEN(n)`
` `
`; Compute the wavelet transform and the power.`
`wave = WV_CWT(data, 'Morlet', 6, /PAD, SCALE=scales)`
`wavePower = ABS(wave^2)`
`; Convert scales to time units.`
`scales *= dt`
` `
`; Contour visualization.`
`c = CONTOUR(wavePower, time, scales, YRANGE=[20,0.25], \$`
`  C_VALUE=FINDGEN(7)+1, \$`
`  /FILL, RGB_TABLE=39, \$`
`  YTITLE='Scale (years)', \$`
`  TITLE='Wavelet Power')`

## Syntax

Result = WV_CWT(Array, Family, Order [, /DOUBLE] [, DSCALE=scalar] [, NSCALE=scalar] [, /PAD] [, SCALE=variable] [, START_SCALE=scalar])

## Return Value

The result is a two-dimensional array of type complex or double complex, containing the continuous wavelet transform of the input Array.

## Arguments

### Array

A one-dimensional array of length N, of floating-point or complex type.

### Family

A scalar string giving the name of the wavelet function to use for the transform.

### Order

The order number, or parameter, for the wavelet function given by Family.

## Keywords

### DOUBLE

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

### DSCALE

Set this keyword to a scalar value giving the spacing between scale values, in logarithmic units. The default is 0.25, which gives four subscales within each major scale.

### NSCALE

Set this keyword to a scalar value giving the total number of scale values to use for the wavelet transform. The default is [log2(N/START_SCALE)]/DSCALE+1.

Set this keyword to force Array to be padded with zeroes before computing the transform. Enough zeroes are added to make the total length of Array equal to the next-higher power-of-two greater than 2N. Padding with zeroes prevents wraparound of the Array and speeds up the fast Fourier transform.

Note: Padding with zeroes reduces, but does not eliminate, edge effects caused by the discontinuities at the start and end of the data.

### SCALE

Set this keyword to a named variable in which to return the scale values used for the continuous wavelet transform. The SCALE values range from START_SCALE up to START_SCALE·2^[(NSCALE–1)DSCALE].

### START_SCALE

Set this keyword to a scalar value giving the starting scale, in non-dimensional units. The default is 2, which gives a starting scale that is twice the spacing between Array elements.

## Reference

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

## Version History

 5.4 Introduced