functionwavDec

Wavelet multilevel decomposition

Information

This function carries out multi-level wavelet decomposition.

Parameter, len, is a vector with (N+2) elements, where N is the number of levels. It contents the length information of the coefficients in all levels. len[1] is the length of the original signal vector; len[2] is the length of the detail coefficient vector of the first decomposition level; len[3] is the length of the detail coefficient vector of the second decomposition level; and so forth. Finally, len[N+2] contains the length of the approximation coefficient vector. Parameter, c, contains the wavelet coefficients of all levels, firstly the first detail level, then the second detail level and so on, and finally the approximation coefficients. This is described again in detail as follows:

Definition of the outputs

Data	Length	Location
Original signal	len[1]	u
First level detail coefficients	len[2]	c[1 : len[2]]
Second level detail coefficients	len[3]	c[len[2]+1 : len[2]+len[3]]
...	...	...
k-th level detail coefficients	len[k+1]	c[sum(len[2:k])+1 : sum(len[2:k+1])]
...	...	...
N-th level detail coefficients	len[N+1]	c[sum(len[2:N])+1 : sum(len[2:N+1])]
Approximation coefficients	len[N+2]	c[sum(len[2:N+1])+1 : sum(len[2:N+2])]

Refer to the section of wavelet Families for the detailed information about the available wavelets.

The default input values provide a quick example with a simple saw-tooth signal.

Inputs

Type	Name	Default	Description
Real[:]	u	{1, 2, 1, 2, 1, 2, 3, 4, 1, 2, 3, 4, 1}	Signal to be analyzed
Integer	N	3	Decomposition level
Real[:]	lod	{0.707, 0.707}	Low pass filter for decomposition
Real[size(lod, 1)]	hid	{-0.707, 0.707}	High pass filter for decomposition

Outputs

Type	Name	Default	Description
Real[:]	c		Detail and approximation coefficients. For data structure see the information section
Integer[N + 2]	len		Lengths of the coefficient vectors of all levels. For data structure see the information section