Wavelet Toolbox Previous page   Next Page
biorfilt

Biorthogonal wavelet filter set

Syntax

Description

The biorfilt command returns either four or eight filters associated with biorthogonal wavelets.

[Lo_D,Hi_D,Lo_R,Hi_R] = biorfilt(DF,RF) computes four filters associated with the biorthogonal wavelet specified by decomposition filter DF and reconstruction filter RF. These filters are

Lo_D
Decomposition low-pass filter
Hi_D
Decomposition high-pass filter
Lo_R
Reconstruction low-pass filter
Hi_R
Reconstruction high-pass filter

[Lo_D1,Hi_D1,Lo_R1,Hi_R1,Lo_D2,Hi_D2,Lo_R2,Hi_R2] = biorfilt(DF,RF,'8') returns eight filters, the first four associated with the decomposition wavelet, and the last four associated with the reconstruction wavelet.

It is well known in the subband filtering community that if the same FIR filters are used for reconstruction and decomposition, then symmetry and exact reconstruction are incompatible (except with the Haar wavelet). Therefore, with biorthogonal filters, two wavelets are introduced instead of just one:

One wavelet, , is used in the analysis, and the coefficients of a signal s are

The other wavelet, psi, is used in the synthesis:

Furthermore, the two wavelets are related by duality in the following sense:

as soon as or and

as soon as .

It becomes apparent, as A. Cohen pointed out in his thesis (p. 110), that "the useful properties for analysis (e.g., oscillations, null moments) can be concentrated in the function; whereas, the interesting properties for synthesis (regularity) are assigned to the psi function. The separation of these two tasks proves very useful."

and psi can have very different regularity properties, psi being more regular than .

The , psi, and phi functions are zero outside a segment.

Examples

See Also
biorwavf, orthfilt

References

Cohen, A. (1992), "Ondelettes, analyses multirésolution et traitement numérique du signal," Ph. D. Thesis, University of Paris IX, DAUPHINE.

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


Previous page  besttree biorwavf Next page

© 1994-2005 The MathWorks, Inc.