upcoef (Wavelet Toolbox)

Direct reconstruction from 1-D wavelet coefficients

Syntax

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,Lo_R,Hi_R)

Description

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).

Examples

% 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.

Algorithm

upcoef is equivalent to an N time repeated use of the inverse wavelet transform.

See Also
idwt

treeord upcoef2