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Extract 1-D approximation coefficients
Syntax
A = appcoef(C,L,'wname',N) A = appcoef(C,L,'wname') A = appcoef(C,L,Lo_R,Hi_R) A = appcoef(C,L,Lo_R,Hi_R,N)
Description
appcoef is a one-dimensional wavelet analysis function.
appcoef computes the approximation coefficients of a one-dimensional signal.
A = appcoef(C,L,'wname',N) computes the approximation coefficients at level N using the wavelet decomposition structure [C,L] (see wavedec for more information).
'wname' is a string containing the wavelet name. Level N must be an integer such that 0 
N length(L)-2.
A = appcoef(C,L,'wname') extracts the approximation coefficients at the last level: length(L)-2.
Instead of giving the wavelet name, you can give the filters.
For A = appcoef(C,L,Lo_R,Hi_R) or A = appcoef(C,L,Lo_R,Hi_R,N), Lo_R is the reconstruction low-pass filter and Hi_R is the reconstruction high-pass filter (see wfilters for more information).
Examples
% The current extension mode is zero-padding (see dwtmode).
% Load a one-dimensional signal.
load leleccum; s = leleccum(1:3920);
% Perform decomposition at level 3 of s using db1.
[c,l] = wavedec(s,3,'db1');
% Extract approximation coefficients at level 3, from the
% wavelet decomposition structure [c,l].
ca3 = appcoef(c,l,'db1',3);
% Using some plotting commands,
% the following figure is generated.
Algorithm
The input vectors C and L contain all the information about the signal decomposition.
Let NMAX = length(L)-2; then C = [A(NMAX) D(NMAX) ... D(1)] where A and the D are vectors.
If N = NMAX, then a simple extraction is done; otherwise, appcoef computes iteratively the approximation coefficients using the inverse wavelet transform.
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