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.


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).



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


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


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


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.


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.



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


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,  9101112131415]
   \ /     \ /     \ /     \ /     \ /     \ /     \ /     \ /
  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 ]

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See Also