ANALYSIS OF CERTAIN WEIGHT FUNCTIONS (WINDOWS) AND THEIR APPROXIMATIONS FOR IMPLEMENTATION OF CONTROLLED RECURSIVE LOW-PASS FILTERS WITH A FINITE IMPULSE RESPONSE ON THEIR BASIS

Abstract

There are various types of weighting functions, the so-called windows in digital signal processing,
such as rectangular (Dirichlet window), triangular (Bartlett window), Vallee-Poussin window,
Kaiser-Bessel window, Barsilon-Temesh window, Hann, Bohman, Blackman, Gauss (Weierstrass),
Dolph - Chebyshev, Hamming windows and many others and ideal characteristics of standard filters
such as low-pass, high-pass, bandpass filters. The purpose of this review article is to determine the most
suitable weighting function for implementation on its basis of a controlled recursive low-pass filter with
a finite impulse response. This article presents an analysis of only some of the above windows and their
approximations, namely the Dolph - Chebyshev window, the Gauss (Weierstrass) window and the
Hamming window. In addition to the analysis, the synthesis of recursive filters with a finite impulse
response for weighting data based on the selected windows and their approximations was considered.
The method of synthesis of Dolph-Chebyshev windows is considered. The implementation of the Gauss
(Weierstrass) window is considered. Methods for approximating the Hamming window and methods
and several algorithms for developing filters with FIR in the form of this window are considered. The
estimation of parameters dependencies some quick window of the maximum level of the side lobes.
Based on the data obtained, conclusions were drawn about the selection of the most suitable and
demonstrating maximum performance windows, suitable for implementation on its basis of a controlled
recursive low-pass filter with a finite impulse response.