  We propose an efficient method for demodulation of phase modulated signals
via iterated Hilbert transform embeddings. We show that while a usual approach
based on one application of the Hilbert transform provides only an
approximation to a proper phase, with iterations the accuracy is essentially
improved, up to precision limited mainly by the discretization effects. We
demonstrate that the method is applicable to arbitrarily complex waveforms, and
to modulations fast compared to the basic frequency. Furthermore, we develop a
perturbative theory applicable to simple cosine waveforms, showing convergence
of the technique.
