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Polynomial Smoothing Splines

2014

Interpolating splines is a perfect tool for approximation of a continuous-time signal \(f(t)\) in the case when samples \(x[k]=f(k),\;k\in \mathbb {Z}\) are available. However, frequently, the samples are corrupted by random noise. In such case, the so-called smoothing splines provide better approximation. In this chapter we describe periodic smoothing splines in one and two dimensions. The SHA technique provides explicit expression of such splines and enables us to derive optimal values of the regularization parameters.