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This collection of Matlab functions calculate symmetric exponential splines. In particular, they compute the values of a Sobolev space reproducing kernel, which is also the autocorrelation of an ARMA process. The functions also compute the values of the corresponding B-spline and the associated interpolation function.
The files are:
|An example of exponential splines. The reproducing kernel φ(t) has a rational Laplace transform, and the coefficients of its polynomials provide the parameterization of the spline. Shown here is the reproducing kernel of a Sobolev space that has three poles (-1-i, -1+i, -1). The function β(t) is the associated B-spline and ψ(t) is the interpolation function|
H. Kirshner, S. Maggio, M. Unser, "A Sampling Theory Approach for Continuous ARMA Identification," IEEE Transactions on Signal Processing, vol. 59, no. 10, pp. 4620-4634, October 2011
H. Kirshner, M. Porat, "On the Role of Exponential Splines in Image Interpolation," IEEE Transactions on Image Processing, vol. 18, no. 10, pp. 2198-2208, October 2009
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