NONUNIFORM p - TIGHT WAVELET FRAMES ON POSITIVE HALF LINE

NONUNIFORM p - TIGHT WAVELET FRAMES ON POSITIVE HALF LINE

O. Ahmad, N. Ahmad

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Abstract

Wavelet frames have gained considerable popularity during the past decade, primarily due to their substantiated applications in diverse and widespread  elds 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  lter 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.

Keywords

Wavelet frame, Walsh functions, Walsh-Fourier transform.