A robust one-dimensional regressive discrete Fourier series

Abstract

The regressive discrete Fourier series (RDFS) proposed in the early nineties can be used to smooth signals in one or two dimensions and to compute derivatives (e.g., spatial or time). This can be useful in applications where there is a need to compute derivatives of noisy data. The choice of the period and number of frequency lines of the Fourier series in the RDFS is empirical, based on the a priori information available about the data being treated. When the chosen period is larger that the data extension and the number of frequency lines increase, the RDFS may present numerical instability. In this paper a more robust RDFS is proposed to avoid such numerical instability. This robust version of the RDFS may be useful when a priori information is not available to guide the choice of the RDFS parameters.