1-D approximation coefficients
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)
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).
This example shows how to extract the level 3 approximation coefficients.
Load the signal consisting of electricity usage data.
load leleccum; sig = leleccum(1:3920);
Obtain the DWT down to level 5 with the 'sym4' wavelet.
[C,L] = wavedec(sig,5,'sym4');
Extract the level-3 approximation coefficients. Plot the original signal and the approximation coefficients.
Lev = 3; a3 = appcoef(C,L,'sym4',Lev); subplot(2,1,1) plot(sig); title('Original Signal'); subplot(2,1,2) plot(a3); title('Level-3 Approximation Coefficients');
You can substitute any value from 1 to 5 for Lev to obtain the approximation coefficients for the corresponding level.
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.