New definition of cepstral calculus

The paper introduces a general definition of the differential cepstrum. It is based on interpolation in the frequency-domain and does not suffer from signal singularities, i.e. zeros on the unit circle, although calculated by the FFT. The approach is used in construction of a novel computational algorithm that produces an asymptotically exact differential cepstrum with no limitations. In an iterative procedure, it eliminates cepstral aliasing and separates causal and anticausal cepstral parts. Its computational complexity is at least four times lower than that of other known algorithms used to decrease cepstral aliasing, while it has no additional storage demands. The result is easily extended to the complex and real cepstrum