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12
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vol 63 / December, 2020
Article

DOI 10.17586/0021-3454-2016-59-3-211-218

UDC 519.61; 004.02; 004.67

ON REDUCTION OF SPACE DIMENSION AT DIGITAL SIGNALS CORRELATION AND CONVOLUTION

A. Y. Grishentsev
ITMO University, Saint Petersburg, 197101, Russian Federation; Associate professor


A. G. Korobeynikov
Saint Petersburg Branch Organization of the Russian Academy of Sciences “Institute of Earth Magnetism, Ionosphere and Radio waves named after N.V. Pushkov RAS”;ITMO University, Saint Petersburg, 197101, Russian Federation ; Deputy Director for Science


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Abstract. Theorems on reduction of space dimension at correlation and convolution of n-dimensional digital signals are formulated and proved, specifically for fast convolution on the base of the fast Fourier transformation. Several examples are presented as illustrations. The theorems are reported to have possible applications in the problems of digital processing of n-dimensional signal, broadband radio communication, optoelectronics, in solitary waves (solitons) research, and in other fields of fundamental and applied natural sciences.
Keywords: correlation, convolution, fast convolution, multi-dimensional signals, optimization of computing, digital signal processing, broadband signals

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