Multi-phase/multi-level modulation data signals recorded on tape after conversion from original digital data are first converted to complex digital signals in an analog-to-digital converter in which the sampling rate is set by a pulse generator frequency controlled by the received signals through a control loop which develops a frequency control voltage (A). The complex digital signals have their real and imaginary parts separately filtered by filters of variable propagation time, but of constant bandwidth to produce complex signals to which the nearest permissible output complex signal (reference signal) is selected by a decision circuit (17), for final conversion to binary signals by a decoder (19) and a shift register (20). Timing shift correction is based on comparison of the received signals and reference signals of the decision stage to produce a control signal (.phi.) which further processed by addition to its previous value to produce a timing correction signal (A) which is applied both to the pulse generator for the sampling frequency of the analog-to-digital converter and to control the propagation time of digital non-recursive filters (14, 15). The timing correction signal (A) control of the filter propagation time makes possible a rapid timing shift correction that overcomes tape jitter effects. It is not necessary to stabilize the received carrier frequency because the tap recording preserves the relation between the sampling/keying frequency and the carrier frequency.