Peculiarities of Applying Partial Convolutions to the Computation of Reduced Numerical Convolutions
Suleimenov I. Kadyrzhan A. Matrassulova D. Vitulyova Y.
July 2024Multidisciplinary Digital Publishing Institute (MDPI)
Applied Sciences (Switzerland)
2024#14Issue 14
A method is proposed that reduces the computation of the reduced digital convolution operation to a set of independent convolutions computed in Galois fields. The reduced digital convolution is understood as a modified convolution operation whose result is a function taking discrete values in the same discrete scale as the original functions. The method is based on the use of partial convolutions, reduced to computing a modulo integer (Formula presented.), which is the product of several prime numbers: (Formula presented.). It is shown that it is appropriate to use the expansion of the number (Formula presented.), to (Formula presented.), where (Formula presented.) is an additional prime number, to compute the reduced digital convolution. This corresponds to the use of additional digits in the number system used to convert to partial convolutions. The inverse procedure, i.e., reducing the result of calculations modulo q to the result corresponding to calculations modulo (Formula presented.), is provided by the formula that used only integers proved in this paper. The possibilities of practical application of the obtained results are discussed.
algebraic rings , computation modulo a prime number , convolution theorem , Galois fields , idempotent elements , moving average method , partial convolutions
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National Engineering Academy of the Republic of Kazakhstan, Almaty, 050010, Kazakhstan
Institute of Communication and Space Engineering, Almaty University of Power Engineering and Telecommunication Named Gumarbek Daukeev, Almaty, 050013, Kazakhstan
National Scientific Laboratory for the Collective Use of Information and Space Technologies (NSLC IST), Satbayev University, Almaty, 050013, Kazakhstan
National Engineering Academy of the Republic of Kazakhstan
Institute of Communication and Space Engineering
National Scientific Laboratory for the Collective Use of Information and Space Technologies (NSLC IST)
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