Minimum-energy wavelet frames generated by the Walsh polynomials

Abstract

Drawing inspiration from the construction of tight wavelet frames generated by the Walsh polynomials, we introduce the notion of minimum-energy wavelet frames generated by the Walsh polynomials on positive half-line R+ using unitary extension principles and present its equivalent characterizations in terms of their framelet symbols. Moreover, based on polyphase components of the Walsh polynomials, we obtain a necessary and sufficient condition for the existence of minimum-energy wavelet frames in L2(R+). Finally, we derive the minimum-energy wavelet frame decomposition and reconstruction formulae which are quite similar to those of orthonormal wavelets on local fields of positive characteristic.