Wavelet Toolbox™

Multisignal 1-D wavelet reconstruction

Syntax

• X = mdwtrec(DEC)
  X = mdwtrec(DEC,IDXSIG) 
  Y = mdwtrec(DEC,TYPE,LEV) 
  A = mdwtrec(DEC,'a')
  A = mdwtrec(DEC,'a',LEVDEC)
  D = mdwtrec(DEC,'d')
  CA = mdwtrec(DEC,'ca')
  CA = mdwtrec(DEC,'ca',LEVDEC)
  CD = mdwtrec(DEC,'cd',MODE)
  CFS = mdwtrec(DEC,'cfs',MODE)
  Y = mdwtrec(...,IDXSIG)
  

Description

X = mdwtrec(DEC) returns the original matrix of signals, starting from the wavelet decomposition structure DEC (see mdwtdec).

X = mdwtrec(DEC,IDXSIG) reconstructs the signals whose indices are given by the vector IDXSIG.

Y = mdwtrec(DEC,TYPE,LEV) extracts or reconstructs the detail or approximation coefficients at level LEV depending on the TYPE value. The maximum value for LEV is LEVDEC = DEC.level.

When TYPE is equal to:

• 'cd' or 'ca', coefficients of level LEV are extracted.
• 'd' or 'a', coefficients of level LEV are reconstructed.
• 'a' or 'ca', LEV must be such that 0 LEV LEVDEC.
• 'd' or 'cd', LEV must be such that 1 LEV LEVDEC.

A = mdwtrec(DEC,'a') is equivalent to A = mdwtrec(DEC,'a',LEVDEC).

D = mdwtrec(DEC,'d') returns a matrix containing the sum of all the details, so that X = A + D.

CA = mdwtrec(DEC,'ca') is equivalent to CA = mdwtrec(DEC,'ca',LEVDEC).

CD = mdwtrec(DEC,'cd',MODE) returns a matrix containing all the detail coefficients.

CFS = mdwtrec(DEC,'cfs',MODE) returns a matrix containing all the coefficients.

For MODE = 'descend'the coefficients are concatened from level LEVDEC to level 1 and MODE = 'descend' concatenates from level 1 to level LEVDEC). The default is MODE = 'descend'. The concatenation is made row-wise if DEC.dirDEC = 'r' or column-wise if DEC.dirDEC = 'c'.

Y = mdwtrec(...,IDXSIG) extracts or reconstructs the detail or the approximation coefficients for the signals whose indices are given by the vector IDXSIG.

Examples

• % Load original 1D-multisignal.
  load thinker
  
  % Perform a decomposition at level 2 using wavelet db2.
  dec = mdwtdec('r',X,2,'db2');
  
  % Reconstruct the original matrix of signals, starting from 
  % the wavelet decomposition structure dec.
  XR = mdwtrec(dec);
  
  % Compute the reconstruction error. 
  errREC = max(max(abs(X-XR)))
  
  errREC =
    2.1026e-010
  
  % Reconstruct the original signal 31, the corresponding 
  % approximation at level 2, details at levels 1 and 2. 
  Y = mdwtrec(dec,31);
  A2 = mdwtrec(dec,'a',2,31);
  D2 = mdwtrec(dec,'d',2,31);
  D1 = mdwtrec(dec,'d',1,31);
  
  % Compute the reconstruction error for signal 31. 
  errREC = max(abs(Y-A2-D2-D1))
  
  errREC =
    6.8390e-014
  

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, waverec

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