Smoothing digital filters with finite memory based on a polynomial approximation of data / V. V. Tikhomirov. // Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika. 2012. № 2. P. 62-65 [Moscow Univ. Math. Bulletin. Vol. 72, N 2, 2017. P. 0].
Digital filters based on polynomial approximation are used to estimate the low-frequency component of a broadband signal and its derivatives. The simplest digital filter is an arithmetical mean algorithm. The filter properties important for applications are associated with the types of transfer functions. Explicit formulas are given for the transfer functions of such filters used to estimate the constant component of an input signal and its first and second derivatives for the second- and third-degree polynomial approximation.
Key words: random sequence, polynomial approximation, least-squares method, finite-memory digital filter, weight function, transfer function, frequency domain.