Applications of a Theorem of Titchmarsh to Bandlimit Irreducibility of Memoryless Transformations

Abstract

Applying Titchmarsh’s result that a signal’s effective bandwidth is proportional to the zero density of its analytic continuation, we show that some fundamental classes of signals possessing $\Omega $for an effective bandlimit cannot be categorically transformed to a class of signals with a smaller bandlimit by an invertible memoryless transformation (nonlinear and/or time-varying).