Analytical Construction and Fast Computation of Frequency Warping Operators and Dual Frame

Abstract

Frequency warping has been introduced as a unitary operator over a nonfinite domain. In practical applications, the need of a feasible implementation forces to redefine frequency warping over finite domains in the framework of redundant transformations called frames, where the unitary property is replaced by the tight frame property, i.e., the adjoint operator behaves as pseudo-inverse. In case a tight frame cannot be designed, inversion can be achieved by finding the dual frame. In this work, with reference to nonsmooth warping functions, we present a new approach to the construction and fast computation of the dual frame operator based on an operator power series. With respect to previous approaches, many limitations are overcome while maintaining important properties of frequency warping.