Abstract: A method and apparatus for estimating the phase differential of a transmitted electromagnetic signal from the amplitude envelope of the signal. The apparatus includes a sampler, phase estimator and demodulator. The phase estimator uses a Hilbert transform or an approximation of the Hilbert transform to estimate the phase differential. The method may be applied to time domain or frequency domain signals. The phase differential is estimated by taking the differential of a function of the envelope, and applying the Hilbert transform to this differential. The resulting phase differential, after correction for sign ambiguity may be used to demodulate the received signal.