The WV_PWT function returns the partial wavelet transform of the input vector A. The transform is done using a user-inputted wavelet filter. WV_PWT is called by WV_DWT .

WV_PWT is based on the routine pwt described in section 13.10 of Numerical Recipes in C: The Art of Scientific Computing, 2nd ed. (Cambridge University Press), and is used by permission.

## Syntax

Result = WV_PWT( A, Scaling, Wavelet, Ioff, Joff [, /DOUBLE] [, /INVERSE] )

## Return Value

The result is an output vector of the same length as A, containing one stage of the pyramidal algorithm (Mallat 1989).

## Arguments

### A

The input vector. The length must be either less than four (4) or a power of two (2).

### Scaling

A vector of scaling (father) coefficients, of length N.

### Wavelet

A vector of wavelet (mother) coefficients, of length N.

### Ioff

An integer that specifies the support offset for Scaling. To center the scaling function over each point in Array, set Ioff to –N/2+2.

### Joff

An integer that specifies the support offset for Wavelet. To center the wavelet function over each point in Array, set Joff to –N/2+2.

## Keywords

### DOUBLE

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

### INVERSE

If set, the inverse transform is computed. By default, the forward transform is computed.

## Method and Result Format

The WV_PWT function computes the wavelet coefficients for one level of the pyramidal algorithm. For a one-dimensional vector with 16 elements, one level of the pyramid appears below:

`Array elements`
`[ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15]`
`   \ /     \ /     \ /     \ /     \ /     \ /     \ /     \ /`
`  s0,d0   s1,d1   s2,d2   s3,d3   s4,d4   s5,d5   s6,d6   s7,d7`

where Si and Di are the scaling and wavelet coefficients and i represents the position. The wavelet coefficients are stored in Result in the following order:

`Result = [ s0, s1, s2, s3, s4, s5, s6, s7,`
`  d0, d1, d2, d3, d4, d5, d6, d7 ]`

## Version History

 5.3 Introduced