Nonuniform p - tight wavelet frames on positive half line

Abstract

Wavelet frames have gained considerable popularity during the past decade, primarily due to their substantiated applications in diverse and widespread fields of engineering and science. Tight wavelet frames provide representations of signals and images where repetition of the representation is favored and the ideal reconstruction property of the associated filter bank algorithm, as in the case of orthonormal wavelets is kept. The main objective of this paper is to introduce a notion of nonuniform wavelet system in L² (R⁺) and provide a complete characterization of such systems to be tight nonuniform wavelet frames in L² (R⁺) by using Walsh-Fourier transform.