XploRe Help: invfwt

Group:	Mathematical Functions
Subgroup:	Fourier and Wavelet transforms
See also:	fwt dwt invdwt fwtin invfwtin fwtinshift fwt2 invfwt2

Function:		invfwt
Description:		invfwt computes the Fast Wavelet Transformation of a vector.

Usage:	`x = invfwt (a, b, n, l, h)`
Input:
	`a`	l x 2 matrix, indices and coefficients of father wavelet
	`b`	(n-l) x 3 matrix, indices and coefficients of mother wavelet
	`n`	integer, total amount of coefficients, has to be a power of 2
	`l`	integer, the number of coeffients of the mother wavelets
	`h`	m x 1 vector, wavelet basis
Output:
	`x`	n x 1 vector,

Notes:: The matrix a contains in the first column the index of the coefficient of the father wavelet and in the second column the coefficient itself. The matrix b contains in the first two columns the indices of the coefficient of the mother wavelet and in the third column the coefficient itself. Both can be retrieved by fwt.
To get the vectors of the wavelet basis, the library wavelet has to be loaded. h can be daubechies2,4,6,8,10,12,14,16,18,20, symmlet4 to 10 or coiflet1 to 5.

Example:

library ("wavelet") x = (0:1023)/1023 {a, b} = fwt (x, 4, daubechies4) sum (x - invfwt (a, b, 1024, 4, daubechies4))

Result:

Content of object sum 

[1,]  1.6205e-12

Group:	Mathematical Functions
Subgroup:	Fourier and Wavelet transforms
See also:	fwt dwt invdwt fwtin invfwtin fwtinshift fwt2 invfwt2