Exploring upper bounds on the number of distinguishable classes

Information theoretic upper bounds on the number of distinguishable classes enable assessments of feasibility when applying classification techniques [1][2]. A goal of this paper is to examine the behavior of these upper bounds as the items being classified become more complex in the sense that the number of degrees of freedom increases. We synthesize filters with different numbers of stages to represent items with various levels of complexity. Using a typical distribution for component tolerances, we study whether different instantiations of filters with greater numbers of components (stages) are more distinguishable than filters with fewer components. We examine the behavior of the Fano upper bound for the number of distinguishable classes as a function of signal-to-noise ratio (SNR), to make the comparisons.