While representations of the $O_N$ algebras are of interest in their own right, as part of operator algebra theory, they have many applications as well: e.g., in a variety of contexts, they enter into the analysis of systems of non-commuting operators; again a subject of independent interest. Because of joint work between the speaker and Bratteli and Dutkay, we shall here focus on such systems that arise in a particular application, that of sub-band filters from signal processing. We shall give an account of joint results on the use of representations of the Cuntz relations $O_N$ (so a particular systems of non-commuting operators); those that arise in an important class of filter problems (even including the study of fractals, and geometric measure theory). This versatility is not surprising since Cuntz algebras, as C*-algebras are infinite, defined from certain relations, and of course simple. By their nature, these representations reflect intrinsic selfsimilar inherent in the problem at hand; and thus they serve ideally to encode sub-bands, and more generally iterated function systems (IFSs), their dynamics, and their measures. At the same time, the $O_N$ -representations offer a new harmonic analysis of signals. Although the Cuntz-algebras initially entered into the study of operator-algebras and physics, in recent years these same Cuntz algebras, and their representation, have found increasing use in applied problems, such as wavelets, fractals, and signals.