Position measuring method and position measuring system used in the multiplication of signal periods

The invention relates to a position measuring device and a position measuring system that are used to process signals (SIN, COS), which represent the displacement of a scale gradation relative to a signal generation unit. To increase the resolution of the signals (SIN, COS), output signals (SIN′, COS′), which have a higher frequency or multiplied number of signal periods in relation to the input signals (SIN, COS), are generated by the device. This enables evaluation units that are connected downstream to record the position and speed of the scale gradation more accurately. The number of signal periods is increased by the calculation of a position signal (POS) with a subsequent filtration or error correction from the input signals (SIN, COS) and by the reading of stored tables of output tables of output signals (SIN′, COS′) in accordance with the calculated position signal (POS).