Irregular sampling for spline wavelet subspaces

Spline wavelets ψ_m(t) are important in time-frequency localization due to (i) ψ_m can be arbitrarily close to the optimal case as m is sufficiently large, (ii) ψ_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⩾3 in the sense of iterative construction and the sampling density δ_m is estimated