# Documentation

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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 character vector 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. ```

## Algorithms

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