Theorem on reducing the dimensionality of space in correlation and convolution

 

 A. U. Grishentcev 

Saint Petersburg National Research University of Information Technologies, Mechanics and Optics

 

The paper is received on January 21, 2015

 

Abstract. In this paper we formulate and prove theorems about reducing the space dimension and the correlation with the convolution of n-dimensional sequences. As an illustration, we consider some examples. These theorems can be widely used in the problems of digital signal processing, broadband radio, studies solitary waves (solitons) and other applied and theoretical natural science fields.

Keywords: correlation, convolution, multi-dimensional signals, the optimization of computing, digital, broadband signals.