ABSTRACT
This chapter describes mapping from monomials to polynomials with respect to the novel application of quantum mechanical methods to signal processing across a range of interdisciplinary research fields. The orthogonal characteristic polynomials or eigenpolynomials play one of the central roles in spectral analysis, since they form a basis due to the completeness relation. They can be computed either via the Lanczos recursion or from the power series representation. The latter method generates the expansion coefficients through the recursion.
