Encoder, motor with encoder, servo system, and signal processing method for encoder

An encoder includes a measurement target which is coupled to a motor, a module which is positioned relative to the measurement target and generates signals based on motion of the measurement target, and a control device which generates and outputs position data based on the signals from the module and includes a position detector, an abnormality detector, a cause analyzer, a non-volatile memory, and a non-volatile memory controller. The position detector detects a position of the motor, the abnormality detector detects an abnormality based on state information including a state of the position detector, the cause analyzer analyzes the state information when the abnormality detector detects the abnormality such that a cause of the abnormality detected by the abnormality detector is identified, and the non-volatile memory controller stores in the non-volatile memory a result of analysis obtained by the cause analyzer.