Abstract: In a method and apparatus for decoding data recorded on magnetic storage medium such as a "swipe card" to yield decoded data values, a magnetoresistive sensor is used to read the data as a pulse stream from the medium and to measure the widths of the received pulses. The data is preferably stored in the medium by the technique of two-frequency phase coherent recording (F2F). By comparing the widths of pulses to be decoded with the widths of previously read pulses to which data values have already been allocated circuitry for derivin a clock signal from a self-clocking recorded signal can be dispensed with. Pulse widths may be measured by monitoring the output of counters (20) incremented by a fast clock for the duration of each pulse, and the pulse widths are compared by comparing counter outputs stored in a memory (28) using a microprocessor (26).