## Improving Calculation Accuracy of Digital Filters Based on Finite Field Algebra  
**[PERSON] 1\({}^{\copyright}\)**, [PERSON] 2, [PERSON] 3, [PERSON] 4,  
**[PERSON] 1,5 and [PERSON] 1,6,*()**  
1 Department of Automation and Control Processes, Saint Petersburg Electrotechnical University \"LETI\", 197376 Saint Petersburg, Russia; [EMAIL_ADDRESS] (D.K.); [EMAIL_ADDRESS] (P.L.)  
2 Scientific Research Institute of System Analysis, Russian Academy of Sciences, 117218 Moscow, Russia; [EMAIL_ADDRESS]  
3 Military Academy after Peter the Great, 142210 Serpuhov, Russia; [EMAIL_ADDRESS]  
4 Laboratory of Computer Security Problems, Saint Petersburg Institute for Informatics and Automation of the Russian Academy of Sciences, 199178 Saint Petersburg, Russia; [EMAIL_ADDRESS]  
5 Department of Applied Mathematics and Mathematical Modeling, North-Caucasus Federal University, 355009 Stavropol, Russia  
6 Youth Research Institute, Saint Petersburg Electrotechnical University \"LETI\", 197022 St. Petersburg, Russia  
* Correspondence: [EMAIL_ADDRESS]  
Received: 18 November 2019; Accepted: 17 December 2019; Published: 19 December 2019  
**Featured Application: Nowadays digital filters are widely used in receivers of different software-defined radio (SDR) communication systems. The main factor affecting the development of SDR is the characteristics of analog-to-digital and digital-to-analog converters. SDR technology allows us to replace existing and developed designs of receivers and transceivers of a heterodyne structure with a limited number of hardware units controlled by specialized software. This helps to simplify the constructions, make them cheaper, improve their performance, and support any modulation types. Furthermore, such an approach can be fruitful in signal reception and demodulation for different types of digital modulations such as DPSK, QAM, GMSK, etc. The main operations in the SDR receiver are heterodyning and filtering, which are performed digitally. In this case, digital filtering determines almost all parameters of the output channel of such a receiver. Therefore, the parameters of digital filters in these receivers have to meet more strict requirements, including the accuracy of calculations and hardware costs. The use of finite field algebra will significantly increase the accuracy of calculations in digital filters of such receivers and reduce hardware costs.**  
**Abstract: The applications of digital filters based on finite field algebra codes require their conjugation with positional computing structures. Here arises the task of algorithms and structures developed for converting the positional notation codes to finite field algebra codes. The paper proposes a method for codes conversion that possesses several advantages over existing methods. The possibilities and benefits of optimization of the computational channel structure for digital filter functioning based on the codes of finite field algebra are shown. The modified structure of computational channel is introduced. It differs from the traditional structure by the fact that there is no explicit code converter in it. The main principle is that the \"reference\" values of input samples, which are free from the error of the analog-digital converter, are used as input samples. The proposed approach allows achieving a higher quality of signal processing in advanced digital filters.**  
**Keywords: digital filter; finite field algebra; conversion device; module; memory device; residue**