Abstract: The frequency of a local clock in the receiving modem is selected to be one half of the sum of the frequency of the mark tone and the frequency of the space tone. The received tones are converted into digital words and the phase of each sample of a digital word is calculated relative to the modem clock. A predetermined number of the phase calculations are stored and the difference between one phase calculation and another phase calculation is made. The number of samples between the one and another is selected such that the difference calculation results in an approximately +90 degrees if the samples represent a mark tone and approximately -90 degrees if the samples represent a space tone. Thus, the sign of the phase difference calculation is determinative of the tone being received.