A data storage device is disclosed comprising at least one head configured to access a magnetic tape comprising a plurality of servo frames each comprising a plurality of servo stripes. The servo stripes are read using the head to generate a read signal that is processed to generate a position error signal (PES). The head is positioned relative to the magnetic tape based on the PES, and the read signal is demodulated into digital data based on a number of servo stripes detected in each servo frame.