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Delta-operator in the design of digital systems on low-bit computers

Karimov Timur Iskandarovich

Assistant, Department of CAD, Ulyanov (Lenin) St. Petersburg State Electrotechnical University "LETI" 

197022, Russia, g. Saint Petersburg, ul. Professora Popova, 5, aud. 1152

carimus@gmail.com
Karimov Artur Iskandarovich

Assistant, Department of CAD, Ulyanov (Lenin) St. Petersburg State Electrotechnical University "LETI"

197022, Russia, g. Saint Petersburg, ul. Professora Popova, 5, aud. 1152

art.krmv@gmail.com
Butusov Denis Nikolaevich

PhD in Technical Science

Associate Professor, Department of CAD, Ulyanov (Lenin) St. Petersburg State Electrotechnical University "LETI"

197022, Russia, g. Saint Petersburg, ul. Professora Popova, 5, aud. 1152

butusovdn@mail.ru
Sol'nitsev Remir Iosifovich

Doctor of Technical Science

Professor, Department of CAD, Ulyanov (Lenin) St. Petersburg State Electrotechnical University "LETI"

197022, Russia, g. Saint Petersburg, ul. Professora Popova, 5, aud. 1152

remira70@mail.ru
Bulakhov Artem Viktorovich

Postgraduate Student, Department of Computer-Aided Design Systems,  Ulyanov (Lenin) St. Petersburg State Electrotechnical University "LETI" 

197022, Russia, g. Saint Petersburg, ul. Professora Popova, 5, aud. 1151

bulahov.a@visteh.ru
Sigaeva Mariya Sergeevna

Assistant, InYaZ Department, Ulyanov (Lenin) St. Petersburg State Electrotechnical University "LETI"

197022, Russia, g. Saint Petersburg, ul. Professora Popova, 5, aud. 1152

msigaeva@gmail.com

DOI:

10.25136/2644-5522.2019.3.21655

Review date:

09-01-2017


Publish date:

19-11-2019


Abstract: The use of low-bit computers is a well-known way to reduce the cost and energy consumption of embedded control and signal processing systems. At the same time, the construction of adequate digital models of dynamic systems on low-discharge computers is hindered by a number of problems associated with the influence of the rounding error of the coefficients. To increase the accuracy of the representation of discrete systems, instead of the traditional z operator, alternative discrete operators can be used, in particular, the δ operator. This mathematical apparatus, in addition, makes it possible to synthesize discrete systems that cannot be realized with a short grid length by standard methods. This article discusses the methodology for using the δ operator in the construction of digital systems on low-bit hardware platforms. The theoretical results obtained are proved analytically and supported by experimental results. The criteria and the preference region for the δ-operator in comparison with the z-operator are shown. The paper considers issues related to the implementation of discrete systems using the δ-operator on low-bit computers with a floating point. In the course of the work, it was found that the accuracy of the machine representation of numbers (digit capacity of the calculator) does not affect the choice of a method for implementing a discrete system. The key parameter when choosing a discrete operator is the sampling rate. A generalized criterion is formulated, which allows one to choose the preferred discrete operator by the type of continuous system and the required sampling frequency.


Keywords: FPGA, Microcontroller, Discrete operator, Linear dynamic systems, Automatic control, Digital signal processing, Delta-operator, Delta-transform, Digital filtering, Finit word length
This article written in Russian. You can find full text of article in Russian here .

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