Certain Matrix Fraction Descriptions (MFDs) are shown to possess important structural properties in their ability to display the infinite pole (respectively zero) structure of a rational transfer function matrix. Among a number of results, two algorithms are developed, the combination of which produce such an MFD displaying the complete infinite frequency structure of a rational transfer function matrix; and a simply checked necessary and sufficient condition for when the given MFD displays the complete infinite pole-zero structure information is provided.