Innokentiy Vasilyevich Semushin, Ulyanovsk State University, Doctor of Science in Engineering, Professor of Information Technology Department at Ulyanovsk State University (UlSU); graduated from V.I. Ul’ianov [Lenin] Leningrad Electrical Engineering Institute, “LETI”, Faculty of Automation Engineering and Computer Science (now Faculty of Computer Science and Technology); author of papers, monographs and textbooks; holds patents for inventions; is interested in filtering and control under uncertainty. [email:
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]I. Semushin


Straightaway Explicit Fir Programming Algorithm for Filtering, Smoothing, and Prediction
In this paper, we develop a straightaway explicit finite impulse response (FIR) programming algorithm for the filtering, smoothing, and prediction of signals containing a nonrandom component or their derivatives as an admissible alternative to previously known methods. The distinctive property of the algorithm is that it determines the FIR directly via the Chebyshev polynomials arising in the finite sample based quadratic approximation numerical analysis thus alleviating the problem of normal equations solution in the ordinary least squares (OLS) method. Using the Chebyshev polynomials gave an option of obtaining the following: short and explicit calculation formulae for FIR, i. e. for the conversion device weighting coefficients, including a possibility of estimating the signal derivatives; short formulae for filterpredictor smoothing factors; necessary memory size design procedure for filterpredictors of arbitrary astaticism order. Results obtained are useful for practical calculations when making a selection of filtering or prediction formula, i.e. while programming a FIR conversion device, and they can find practical use in adaptive devices. Firfilters, transversal filter structure, chebyshev polynomials, filtering, smoothing, prediction, quadratic approximations.

