Close Approximations for Daublets and their Spectra

This paper offers a new regard on compactly supported wavelets derived from FIR filters. Although being continuous wavelets, analytical formulation are lacking for such wavelets. Close approximations for daublets (Daubechies wavelets) and their spectra are introduced here. The frequency detection properties of daublets are investigated through scalograms derived from these new analytical expressions. These near-daublets have been implemented on the MatlabTM wavelet toolbox and a few scalograms presented. This approach can be valuable for wavelet synthesis from hardware or for application involving continuous wavelet-based systems, such as wavelet-OFDM.