Starting from piecewise constant functions, a novel family of generalized symmetric B-splines, with realizable ideal low-pass filters, are constructed. The first order generalized B-spline low-pass filter is closely related to functions analytic in a neighborhood of the unit disc and the generalized sinc functions. The properties of this kind of low-pass filters are investigated. The behavior of the generalized B-spline low-pass filter related to normalized Gaussian distribution is considered.
low-pass filter generalized B-spline analytic function Gaussian distribution
42A38 44A15 62P30 65R10
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