A digital apparatus for data recovery system wherein data is recorded in FM or MFM code on magnetic media, comprises a measuring unit that in correspondence of a read pulse n as an input, supplies as an output, information related to the actual duration of interval N between pulse n and the previous read pulse n-1. A recovery unit for the magnetic media speed error relative to a nominal speed corrects the duration according to a code representative of the magnetic media speed error and a peak shift recovery unit which, according to the peak shift of pulse n-1, determined on the basis of the time history of the most recent pulses n-2, n-3, n-1 and the corrected duration, supplies as an output, nominal duration information related to this corrected duration and information representative of the direction and the amount of the peak shift of said read out pulse N-7. A measuring unit of speed error defines a code representative of the error as a function of the peak shift direction of a suitable number of subsequent read out pulses and a previously measured speed error which is fed to the speed error recovery unit. The nominal duration information is applied to the input of a logic unit for generating a "window" signal and reconstructing the read pulse in suitable phase relationship with the window signal.