A new phase Doppler anemometry (PDA) signal processing method based on a Hilbert transform algorithm is introduced and analysed. By generating a 90 degrees phase-shifted burst signal in the time domain, the envelope of the Doppler burst can be determined. In addition, this envelope is approximated by a Gaussian exponential function. The difference of the maxima of these Gaussian approximations for two related PDA bursts gives an estimate of the time difference between these time-shifted signals. With the introduction of this estimation method, the restriction to the [0,360 degrees] interval resulting from conventional signal analysis may be avoided in many cases. To investigate the dependence on SNR, burst position, burst frequency and sampling rate, results of computer simulations are presented. The feasibility of the method is demonstrated briefly by experimental results. Phase differences of more than 2000 degrees arising from the measurement of monodisperse droplets by a conventional PDA setup could be determined.