Orthogonal and biorthogonal filter banks are arrangements of lowpass, highpass, and bandpass filters that divide your data into subbands. If you do not modify the subbands, these filters enable perfect reconstruction of the original data. In most applications, you process data differently in the different subbands and then reconstruct a modified version of the original data. Orthogonal filter banks do not have linear phase. Biorthogonal filter banks do have linear phase. You can specify wavelet and scaling filters by the number of the vanishing moments, which allows you to remove or retain polynomial behavior in your data. Lifting allows you to design perfect reconstruction filter banks with specific properties.
You can use Wavelet Toolbox™ functions to obtain and use the most common orthogonal and biorthogonal wavelet filters. You can design your own perfect reconstruction filter bank through elementary lifting steps. You can also add your own custom wavelet filters.
- Orthogonal and Biorthogonal Filter Banks
Daubechies' extremal-phase, least-asymmetric, and best-localized wavelets, Fejér-Korovkin filters, coiflets, Han linear-phase filters, Morris minimum-bandwidth filters, Beylkin and Vaidyanathan filters, biorthogonal spline filters
1-D and 2-D lifting, Local polynomial transforms, Laurent polynomials