Data smoothing by cubic spline filters

In this correspondence, a digital filter that allows the computation of a smoothing cubic spline for equispaced data with a constant control parameter is proposed. Filters to compute its first and second derivatives are also presented. Derived from the classical matrix solution, these filters offer an efficient way to calculate smoothed data and its derivatives, especially when the length of data is long. Moreover, these filters have been found to possess several interesting properties. For instance, the smoothing filter is a low-pass filter with the maximum flatness property. In addition, a useful relation between the filter bandwidth and the control parameter is established, which can be used for its optimal choice in practice. The proposed filters can easily be implemented either with a recursive structure for off-line processing or with a nonrecursive implementation for real-time processing.