Close Approximations for Daublets and their Spectra

TL;DR

This paper introduces close analytical approximations for Daubechies wavelets and their spectra, enabling easier analysis and implementation in continuous wavelet systems like wavelet OFDM.

Contribution

It provides new analytical expressions for Daubechies wavelets, facilitating their use in hardware and continuous wavelet applications.

Findings

Close approximations accurately match Daubechies wavelets.

Spectral properties are effectively analyzed using the new expressions.

Implementations in MATLAB demonstrate practical utility.

Abstract

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 Matlab 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.