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Irregular sampling for spline wavelet subspaces

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1 Author(s)
Youming Liu ; Dept. of Appl. Math., Beijing Polytech. Univ., China

Spline wavelets ψm(t) are important in time-frequency localization due to (i) ψm can be arbitrarily close to the optimal case as m is sufficiently large, (ii) ψm 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 δm is estimated

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Information Theory, IEEE Transactions on  (Volume:42 ,  Issue: 2 )