Real-Valued Periodic Wavelets: Construction and Relation with Fourier Series

Abstract

In this paper, we construct the real-valued periodic orthogonal wavelets. The method presented here is new. The decomposition and reconstruction formulas involve only 4 terms respectively. It demonstrates that the formulas are simpler than those in other kinds of periodic wavelets. Our wavelets are useful in applications since it is real-valued. The relation between the periodic wavelets and the Fourier series is also discussed.