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upcoef

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,'wname'',1)
Y = upcoef(O,X,Lo_R,Hi_R)
Y = upcoef(O,X,Lo_R,Hi_R,1)

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.
```