Affine Frames of Rational Wavelets in H2 (II+)
Krishnaprasad, Perinkulam S.
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In this paper we investigate frame decompositions of H2(II+) as a method of constructing rational approximations to nonrational transfer functions in H2(II+). The frames of interest are generated from a single analyzing wavelet. We consider the case in which the analyzing wavelet is rational and show that by appropriate grouping of terms in a wavelet expansion, H2(II+) can be decomposed as an infinite sum of a rational transfer functions which are related to one another by dilation and translation. Criteria for selecting a finite number of terms from such an infinite expansion are developed using time-frequency localization properties of wavelets.