SIMULATION OF DYNAMIC TRANSMISSION COEFFICIENTS OF SECOND-ORDER BUTTERWORTH DIGITAL FILTERS

Abstract

The purpose of the conducted research is to use methods and means of designing digital filters in a dynamic state. This is necessary to reduce the transient processes in second-order Butterworth digital filters, to reduce the dynamic modes of digital circuits, and to determine the expediency of using the dynamic transmission coefficient method. Dynamic errors occur in any linear system with limited bandwidth. Errors reduce the immunity of receiving signals and signals with rapidly changing parameters. Therefore, when performing calculations, it is necessary to take into account transient processes that occur in digital filters. If the parameters of the signal change continuously in time, then these processes can exist indefinitely. Taking into account transient processes, it is necessary to examine all calculations and analysis in a dynamic state. Disadvantages of digital filtering when synthesizing an analog prototype using the method of invariant impulse response are the impossibility of obtaining an infinitely small bandwidth, as well as the presence of the effect of overlapping spectra at the edges of the range due to discretization. Discrete Fourier transforms (direct and inverse) are used to analyze the operation of digital Butterworth filters in a dynamic state. In order to avoid overlapping of spectra, it is proposed to switch to z-transformation, while the denormalization of the transmission coefficients is previously used. The calculations use a coefficient that relates the clock frequency to the cutoff frequency of the filter through the number of samples of the frequency response and through the number of samples within the bandwidth. To solve the problems, a set of methods was used: system analysis – to study the current algorithms for processing transient processes occurring in digital filters; z-transformation – for the synthesis of digital filters; fast Fourier transform and dynamic transmission coefficient – for calculating two-dimensional dynamic characteristics of second-order Butterworth digital filters. The method of synthesizing Butterworth's digital filters was further developed, which allows for time-frequency analysis, which makes it possible to study the dynamic characteristics of digital filters.