Direct reconstruction from 1-D wavelet coefficients

`Y = upcoef(O,X,`

* 'wname'*,N)

Y = upcoef(O,X,

`'wname'`

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'`

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,`

computes
the * 'wname'*,N)

`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,`

computes
the * 'wname'*,N,L)

`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,`

is
equivalent to * 'wname'*')

`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.

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