A new geometric approach to the calculation of transmission zeros in the signal processing theory

Abstract

In the paper, a new method concerning the estimation of transmission zeros is introduced. Following the notion related to the Smith–McMillan-like technique allowing us to determine the crucial zeros, a new solution covering the geometric approach is effectively presented and confirmed in the manuscript. Indeed, the existing non-intuitive method providing non-unique computational effort even for the well-conditioned environmental matrices can successfully be replaced without loss of generality. Therefore, in order to overcome the indicated difficulties, the rank-nullity theorem is adapted to determine the transmissions zeros, for which the matrix depending on variable coefficients loses its rank. The benefits of the new scheme in modeling of non-square MIMO signal processing systems are clearly visible. It should be emphasized that currently only the Smith–McMillan factorization allows us to calculate the transmission zeros. However, in the proposed method, it can be done faster, more intuitively and effectively.