The problem was on a relatively modern aircraft with 2 ADC.The defective ADC showed incorrect data but when the alternate ADC was selected the faulty ADC was still putting out false data to other systems such as autothrust ,altitude alerter etc.There were no failure flags or warnings of any kind on any of the flight instruments just a major discrepancy in speed on the pfd and the altimeter over reading.The faulty ADC recovered itself in the descent at about FL100 and after we had been on the gate a few minutes it eventually produced a failure message.