Reduced hardware costs with software and hardware implementation of digital methods multistage discrete Fourier transform on programmable logic devices
Let us consider questions, which are connected to the research of terms of hardware and software implementation digital signal processing (DSP) methods. Theoretical basis of this research are methods of non-recursive difference of digital filtration with integer difference coefficients different orders of difference and methods of multistage discrete Fourier transform (DFT) based on such digital filtration. The purpose of the study is the research and formalization of necessary and sufficient condition of lowering hardware costs in hardware and software implementation of methods multistage DFT of digital signals on programmable logic devices (PLD). For reaching the research goal there are used methods of direct search and comparative analysis of results of such realization of methods of multi-stage DFT of digital multi-band signals, while filtering these signals, which are based on their non-recursive difference digital filtering with integer difference values coefficients and different orders of magnitude of difference. There are described abilities and specialties of PLD, which are built using architecture of a coarse-grained or fine-grained architecture or using combined architecture, which connects the convenience of implementing digital processing algorithms signals on the basis of tables of code conversion and reconfigurable memory modules. It is clear that a necessary and sufficient condition of lowering hardware costs in terms of hardware and software realization of methods for multi-stage DFT of digital signals on PLD is the triviality of meanings of integer difference coefficients of a non-recursive difference digital high difference orders’ filtration, which ensure this information. There is mentioned a formula, which allows making such condition. The practical significance of the research results consists of defining the necessary and sufficient condition of lowering hardware costs in terms of hardware and software implementation on PLD methods of multi-stage DFT signals based on their non-recursive digital difference filtering with integer values differential coefficients of various orders of magnitude difference. The novelty of research results lies in formalization of this condition. The reliability of the research results confirms their compliance with the results of well-known developments of DSP methods.
Burov, Yu. Ya., & Burova, A. Yu. (2000). Synthesis of the recurrence digital filters. Russian scientific-technical society of radio engineering, electronics and communication named after A. S. Popov: LV Scientific session, dedicated to Radio Day: Theses of reports. Moscow: Russian Scientific and Technical Society of Radiotechnics, Electronics and Communications.
Burova, A. Yu. (2017). Certification of aircraft. Moscow: LENAND.
Burova, A. Yu. (2019). Minimisation of asymmetry of thrust of the dual-flow turbojet engines of the airliner in accordance with the results of the system analysis of the thrust parameters. Asia Life Sciences Supplement, 21(2), 629-643.
Burova, A. (2020). Digital signal processing without performing arithmetic multiplication operations. Amazonia Investiga, 9(25), 200-205. Retrieved from https://www.amazoniainvestiga.info/index.php/amazonia/article/view/1051
Burova, A., & Kabakov, V. (2020). “Unerroric” of multistage discrete Fourier transform of digital signal without arithmetic operations of multiplication. Amazonia Investiga, 9(25), 429-437. Retrieved from https://www.amazoniainvestiga.info/index.php/amazonia/article/view/1092
Kanashchenkov, A. I., Matveev, A. M., & Novikov, S. V. (2018). Measuring System for Use in Radar-System Development. Russian Engineering Research, 38(11), 896-900.
Kaplun, D. I., & Merkucheva, T. V. (2009). New method of filters synthesis on PLD. Radioelectronics issues. Moscow: OJSC “Central Research Institute “Electronics”.
Kuzkin, V. S. (1983). Difference digital filtering. Radiotechnics, 1, 52-54.
Shcherbakov, M. A., Steshenko, V. B., & Gubanov, D. A. (2000). Digital polynomial filtering in real time: algorithms and ways of implementation on PLD. Proceedings of the Third International Conference "DSP and its application" (DSPA’2000), 1, 19-26.
Shinakov, Yu. S., & Burov, Yu. Ya (2000). Method of adaptive multistage shift and filtering of harmonic signal components. Telecommunication, 1, 15-17.
Shinakov, Yu. S., & Burov, Yu. Ya. (1998). Difference digital filtering with integer coefficients. Proceedings of The First International Conference "DSP and its applications" (DSPA’98), 2, 94-99.
Shinakov, Yu. S., Burov, Yu. Ya., & Burova, A. Yu. (2000). Theory, methods and algorithms of difference digital filtering. Proceedings of the Third International Conference "DSP and its application" (DSPA’2000), November 29-December 1, 2000, 1, 96-99.
Speransky, V. S. (1997). DSP and their application for the formation and processing of signals: Training manual. Moscow: Moscow Technical University of Communication and Informatics.
Speransky, V. S. (2008). Signal microprocessors and their application in telecommunication systems and electronics. Moscow: Hot Line - Telecom.
Steshenko, V. B. (2000). PLD implementation by firm ALTERA: designing devices signal processing. Moscow: DODEKA.
Steshenko, V. B. (2007). PLD implementation by firm ALTERA: element base, design system and hardware description languages. Moscow: DODEKA.
Vityazev, V. V. (2017). Multi-speed signal processing. Moscow: Publishing House "Hot Line-Telecom".
Vityazev, V. V., & Vityazev, S. V. (2007). DSP TMS320C67x by Texas Instruments. Ryazan: Ryazan State Radio Engineering University.
Zalmanzon. L.A. (1989). Fourier, Walsh, Haar transforms and their application in control, communication, and other fields. Moscow: Nauka.