PURPOSE: To improve the tracking performance with respect to the transient state by providing a transient change detection section detecting a signal transient change and an input/output deviation detection section detecting the increased deviation in the signal and allowing a processing section to vary the time constant at the detection of transient change.

CONSTITUTION: A transient change detection section 2 obtains a difference between an input signal and an output signal between an input section 1 and a filter processing section 3 and judges it as the occurrence of a transient change if the difference exceeds a reference value. Moreover, an input/output deviation detection section 4 decided it as a large deviation if the integration value of the difference between the input signal and the output signal exceeds a reference value. A processing section 3 has a function having a smooth processing capability in the steady-state but changing the time constant sequentially at the entrance of a detection signal, and then can follow well a rapid transient change as well as a slow transient change. Thus, the titled digital filter acts stably in an alarm device or a control system where a transient change is to be caught surely.