QUATERNION DOMAIN LAPLACE TRANSFORM OF THE PULSES VECTOR

Abstract

Currently, the multi-input-multi-output (MIMO) scheme using complex and hypercomplex signals is widely used in communication theory and technology. This scheme allows to increase the channel capacity and their noise immunity. In the MIMO scheme, the components of the pulse vector are interconnected by a channel matrix. In this regard, the problem arises of obtaining the Laplace transform of such a vector.

In the presented methodology, methods of obtaining the Laplace transform of real signals using a matrix representation of hypercomplex signals were used. Suggested a methodology of obtaining the Laplace transform of a four-dimensional vector of pulses connected by a MIMO scheme. To obtain the Laplace transform, the quaternion in the matrix expansion and the corresponding matrix of quaternion frequencies are used as the kernel of the integral transform. It is shown that to obtain the Laplace quaternion transformation, it is possible to use the well-known transformation formulas, replacing the complex frequency with the quaternion frequency. Examples of the use of the method are presented.