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