Group: Mathematical Functions
Subgroup: Fourier and Wavelet transforms
See also: invfwt dwt invdwt fwtin fwtinshift fwt2
Links:
Wavelet tutorial
Function: fwt
Description: fwt computes the Fast Wavelet Transformation of a vector.
Usage: {a, b} = fwt (x, l, h)
Input:
x n x 1 vector, input data where n has to be a power of 2
l integer, number of father wavelet coefficients
h m x 1 vector, wavelet basis
Output:
a l x 2 matrix, indices and coefficients of the father wavelets
b (n-l) x 3 matrix, indices and coefficients of the mother wavelets
Notes:
For the estimation x have to be the realizations on an equispaced grid. 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. The results for the coefficients differ from dwt by the factor 1/sqrt(n).
Example:
library ("wavelet") 
x = (0:1023)/1023 
{a, b} = fwt (x, 4, daubechies4) 
a
Result:
[1,] 0.000000 0.079014 
[2,] 1.000000 0.204137 
[3,] 2.000000 0.337344 
[4,] 3.000000 0.379505 

The matrix b contains only entries which are approxemately zero.
Group: Mathematical Functions
Subgroup: Fourier and Wavelet transforms
See also: invfwt dwt invdwt fwtin fwtinshift fwt2
© XploRe, generated on 6.3.98 7:17 .