Parametric smoothing of spline interpolation

Cubic spline interpolation is commonly applied in signal reconstruction problems. However, overshooting between samples is normally observed, and typically the reconstructed signal does not preserve the statistical properties of the original data or other desired properties such as monotonicity or convexity. These undesirable effects are minimized in the case of piecewise linear (PWL) interpolation, of course with a discontinuous derivative. In this paper we use a parameterized family of splines, named αsplines, that allows a smooth transition from PWL (α = 0) to cubic spline interpolation (α = 1). Closed-form expressions that relate α to the smoothness and variance of the interpolation are derived. Moreover, a fast interpolation technique based on digital filtering can be applied.