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E-splines

A Mathematica package is made available for the symbolic computation of exponential spline related quantities: B-splines, Gram sequence, Green function, and localization filter.

Description:

To obtain the analytical expressions of cardinal exponential B-splines and other related quantities, we recommend using the Mathematica software package Esplines that is provided below. The spline type in each routine is specified by two list variables: poles, and zeros (which is optional). For example, the cubic B-spline corresponds to the parameters: poles={0,0,0,0} and zeros={}.

The available functions are:

 bullet BsplineE[t, poles, zeros]: Evaluates the generalized B-spline.
 bullet B[z, poles, zeros]: Returns the discrete B-spline filter.
 bullet A[z, poles, zeros]: Returns the z-transform of the Gram sequence of the B-splines.
 bullet Localization[z, poles]: Returns the z-transform of the spline localization operator.
 bullet GreenE[t, poles, zeros]: Evaluates or returns the symbolic form of the Green function, which is obtained by inverse Laplace transformation.

Download:

 bullet E-splines.nb (Mathematica file)