Irregular sampling for spline wavelet subspaces

摘要

Spline wavelets /spl psi//sub m/(t) are important in time-frequency localization due to (i) /spl psi//sub m/ can be arbitrarily close to the optimal case as m is sufficiently large, (ii) /spl psi//sub m/ has compact support and simple analytic expression, which lead to effective computation. Although the spline wavelet subspaces are so simple, Walter's well-known sampling theorem does not hold if the order of spline m is even. Moreover, when irregular sampling is considered in these spaces, it is hard to determine the sampling density, which is a serious problem in applications, in this correspondence, a general sampling theorem is obtained for m/spl ges/3 in the sense of iterative construction and the sampling density /spl delta//sub m/ is estimated.