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The phase synchrony analysis of stochastic time series is considered with a view towards its application in EEG (electroencephalogram) processing. A Phase Synchrony Processor is proposed and its properties are examined on the basis of known signals. The observed dependence of the phase synchrony coefficient on the analysis parameters, such as the filter bandwidth and the length of the time-window, may - especially in low synchrony cases - lead to biased results. The analysis parameters can be chosen judiciously based on the results of a phase synchrony study of artificially generated signals with known phase synchrony. To illustrate the importance of the parameter choices available, a phase synchrony coefficient analysis is presented based on actual EEG.