Dual frame of frequency warping operators

In this work we introduce the dual frame operator relative to the aliasing compensated frequency warping operator for non-smooth warping functions. Except for approximation errors, the resulting operators pair allows perfect reconstruction. Unlike previously introduced frequency warping frame and dual frame pair, which was obtained by adding redundancy to the group delay shift covariance analysis space, in this case no modifications are needed to the analysis operator. Anyway, to calculate the dual frame, previously introduced computational models are exploited and forward developed. Basically, the dual frame construction is based on an operator power series which is entirely precomputed, so the complexity of frequency warping inversion is not increased.