Wavelet Toolbox™

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
mdwtdec, wavedec

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