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Direct reconstruction from 1-D wavelet coefficients
Y = upcoef(O,X,'wname',N)
Y = upcoef(O,X,'wname',N,L)
Y = upcoef(O,X,Lo_R,Hi_R,N)
Y
= upcoef(O,X,Lo_R,Hi_R,N,L)
Y = upcoef(O,X,'wname'')
Y = upcoef(O,X,'wname'',1)
Y = upcoef(O,X,Lo_R,Hi_R)
Y = upcoef(O,X,Lo_R,Hi_R,1)
upcoef is a one-dimensional wavelet analysis function.
Y = upcoef(O,X,'wname',N) computes the N-step reconstructed coefficients of vector X.
'wname' is a string containing the wavelet name. See wfilters for more information.
N must be a strictly positive integer.
If O = 'a', approximation coefficients are reconstructed.
If O = 'd', detail coefficients are reconstructed.
Y = upcoef(O,X,'wname',N,L) computes the N-step reconstructed coefficients of vector X and takes the length-L central portion of the result.
Instead of giving the wavelet name, you can give the filters.
For Y = upcoef(O,X,Lo_R,Hi_R,N) or Y = upcoef(O,X,Lo_R,Hi_R,N,L), Lo_R is the reconstruction low-pass filter and Hi_R is the reconstruction high-pass filter.
Y = upcoef(O,X,'wname'') is equivalent to Y = upcoef(O,X,'wname'',1).
Y = upcoef(O,X,Lo_R,Hi_R) is equivalent to Y = upcoef(O,X,Lo_R,Hi_R,1).
% The current extension mode is zero-padding (see dwtmode). % Approximation signals, obtained from a single coefficient % at levels 1 to 6. cfs = [1]; % Decomposition reduced a single coefficient. essup = 10; % Essential support of the scaling filter db6. figure(1) for i=1:6 % Reconstruct at the top level an approximation % which is equal to zero except at level i where only % one coefficient is equal to 1. rec = upcoef('a',cfs,'db6',i); % essup is the essential support of the % reconstructed signal. % rec(j) is very small when j is ≥ essup. ax = subplot(6,1,i),h = plot(rec(1:essup)); set(ax,'xlim',[1 325]); essup = essup*2; end subplot(611) title(['Approximation signals, obtained from a single ' ... 'coefficient at levels 1 to 6']) % Editing some graphical properties, % the following figure is generated.
% The same can be done for details. % Details signals, obtained from a single coefficient % at levels 1 to 6. cfs = [1]; mi = 12; ma = 30; % Essential support of % the wavelet filter db6. rec = upcoef('d',cfs,'db6',1); figure(2) subplot(611), plot(rec(3:12)) for i=2:6 % Reconstruct at top level a single detail % coefficient at level i. rec = upcoef('d',cfs,'db6',i); subplot(6,1,i), plot(rec(mi*2^(i-2):ma*2^(i-2))) end subplot(611) title(['Detail signals obtained from a single ' ... 'coefficient at levels 1 to 6']) % Editing some graphical properties, % the following figure is generated.