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# mdwtdec

Multisignal 1-D wavelet decomposition

## Syntax

```DEC = mdwtdec(DIRDEC,X,LEV,WNAME) DEC = mdwtdec(DIRDEC,X,LEV,LoD,HiD,LoR,HiR) DEC = mdwtdec(...,'mode',EXTMODE) ```

## Description

`DEC = mdwtdec(DIRDEC,X,LEV,WNAME)` returns the wavelet decomposition at level `LEV` of each row (if `DIRDEC = 'r'`) or each column (if ```DIRDEC = 'c'```) of matrix `X`, using the wavelet `WNAME`.

The output `DEC` is a structure with the following fields:

 `'dirDec'` Direction indicator: `'r'` (row) or `'c'` (column) `'level'` Level of the DWT decomposition `'wname'` Wavelet name `'dwtFilters'` Structure with four fields `LoD`, `HiD`, `LoR` and `HiR` `'dwtEXTM'` DWT extension mode (see `dwtmode`) `'dwtShift'` DWT shift parameter (0 or 1) `'dataSize'` Size of `X` `'ca'` Approximation coefficients at level `LEV` `'cd'` Cell array of detail coefficients, from level 1 to level `LEV`

Coefficients `cA` and ```cD{k} (for k = 1 to LEV)``` are matrices and are stored in rows if `DIRDEC` = `'r'` or in columns if `DIRDEC` = `'c'`.

`DEC = mdwtdec(DIRDEC,X,LEV,LoD,HiD,LoR,HiR)` uses the four filters instead of the wavelet name.

`DEC = mdwtdec(...,'mode',EXTMODE)` computes the wavelet decomposition with the `EXTMODE` extension mode that you specify (see `dwtmode` for the valid extension modes).

## Examples

```% Load original 1D-multisignal. load thinker % Perform a decomposition at level 2 using wavelet db2. dec = mdwtdec('r',X,2,'db2') dec = dirDec: 'r' level: 2 wname: 'db2' dwtFilters: [1x1 struct] dwtEXTM: 'sym' dwtShift: 0 dataSize: [192 96] ca: [192x26 double] cd: {[192x49 double] [192x26 double]} % Compute the associated filters of db2 wavelet. [LoD,HiD,LoR,HiR] = wfilters('db2'); % Perform a decomposition at level 2 using filters. decBIS = mdwtdec('r',X,2,LoD,HiD,LoR,HiR) decBIS = dirDec: 'r' level: 2 wname: '' dwtFilters: [1x1 struct] dwtEXTM: 'sym' dwtShift: 0 dataSize: [192 96] ca: [192x26 double] cd: {[192x49 double] [192x26 double]} ```

## References

Daubechies, I. , Ten lectures on wavelets, CBMS-NSF conference series in applied mathematics. SIAM Ed., 1992.

Mallat, S., “A theory for multiresolution signal decomposition: the wavelet representation,” IEEE Pattern Anal. and Machine Intell., vol. 11, no. 7, 1989, pp. 674–693.

Meyer, Y. , Ondelettes et opérateurs, Tome 1, Hermann Ed. (English translation: Wavelets and operators, Cambridge Univ. Press. 1993.)

## See Also

#### Introduced in R2007a

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