An exact numerical algorithm for computing the unwrapped phase of a finite-length sequence

A direct relationship between a one-dimensional time series and its unwrapped phase was shown by R. McGowan and R. Kuc (1982). They proposed an algorithm for computing the unwrapped phase by counting the number of sign changes in a Sturm sequence generated from the real and imaginary parts of the DFT (discrete Fourier transform). Their algorithm is limited to relatively short sequences by numerical accuracy. An extension of their algorithm is proposed which, by using all-integer arithmetic, permits exact computation of the number of multiples of π which must be added to the principal value of the phase to uniquely give the unwrapped phase of a one-dimensional rational-valued finite-length sequence of arbitrary length. This extended algorithm should be of interest when highly accurate phase unwrapping is required