Irregular sampling for spline wavelet subspaces

Abstract

Spline wavelets m(t) are important in time-frequency localization due to i) r, can be arbitrarily close to the optimal case as m is sufficiently large, ii) i", has compact support and simple analytic expression, which lead to effective computation. Although the spline wavelet subspaces are so simple, Walter's wellknown 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 > 3 in the sense of iterative construction and the sampling density t>m is estimated. Index Terms-Sampling, spline wavelets, algorithm. © 1996 IEEE Publisher Item Identifier S 0018-9448(96)01686-0.