Certain Matrix Fraction Descriptions (MFDs) are shown to possess impor
tant structural properties in their ability to display the infinite po
le (respectively zero) structure of a rational transfer function matri
x. Among a number of results, two algorithms are developed, the combin
ation of which produce such an MFD displaying the complete infinite fr
equency structure of a rational transfer function matrix; and a simply
checked necessary and sufficient condition for when the given MFD dis
plays the complete infinite pole-zero structure information is provide
d.