**Name**

**ibiowave1** Reconstructs a signal from a biorthogonal wavelet transform

**Command Synopsis**

**ibiowave1** [-r *RecursNum*] [-e *EdgeMode*] [-n *FilterNorm*] *WavTrans* *RecompSignal* *ImpulseResponse1* *ImpulseResponse2*

-rRecursNum: Number of levels (default 1)

-eEdgeMode: Edge processing mode (0/1/2, default 2)

-nFilterNorm: Normalization mode for filter bank (0/1/2, default 0)

WavTrans: Input wavelet transform (wtrans1d)

RecompSignal: Reconstructed signal (fsignal)

ImpulseResponse1: Impulse response of filter 1 (fsignal)

ImpulseResponse2: Impulse response of filter 2 (fsignal)

**Function Summary**

void ibiowave1 (NumRec , Edge , FilterNorm , Wtrans , Output , Ri1 , Ri2 )

int *NumRec ;

int *Edge ;

int *FilterNorm ;

Wtrans1d Wtrans ;

Fsignal Output ;

Fsignal Ri1 ;

Fsignal Ri2 ;

**Description**

*ibiowave1* reconstructs a signal from a sequence of sub-signals forming a wavelet decomposition, using filter banks associated to biorthogonal wavelet bases (see [CDF92]).
The notations and definitions have been defined in *owave1* and *biowave1*. The coefficients of the wavelet decomposition
*A*_{J}, *D*_{J}, *D*_{J-1},..., *D*_{1} are stored in a sequence of files whose names obey the syntaxic rules described in *biowave1* module's documentation, and whose prefix is *WavTrans*. The reconstructed signal's coefficients *A*_{0}[*k*] are stored in the file *RecompSignal*.

As for the orthogonal case the inverse wavelet transform is a recursive algorithm. *A*_{j-1} is computed from *A*_{j} and *D*_{j} using the relation :

The edge processing methods are corresponding to those described for *biowave1*.

The complexity of the algorithm is roughly the same as that of *biowave1*.

The sample values of the reconstructed signal are stored in the file *RecompSignal*.

The coefficients (*h*_{k}) and
() of the filter's impulse responses are stored in the file *ImpulseResponse1* and *ImpulseResponse2*.

- The -r option specifies the number of levels
*J*in the decomposition. - The -e option specifies the edge processing mode (see
*biowave1*). - The -n option specifies the normalisation mode of the filter impulse responses' coefficients. It should be selected according to the mode used for the decomposition in order to get exact reconstruction.

**See Also**

**Version 1.3**

Last Modification date : Thu Jan 31 15:05:17 2002

**Author**

Jean-Pierre D'Ales