PURPOSE: To attain a small-sized multi-dimensional filter without delay distortion by constituting the filter with two cyclic filters and two time axis inverting circuits of the same characteristic and passing an output of the cyclic filter through the cyclic filter and the time axis inverting circuit again after passing through the time axis inverting circuit.

CONSTITUTION: An input is given to the cyclic filter 1, where prescribed filtering is attained. The result has delay distortion, however, the distortion is fed to the time axis inverting circuit 2, where the time axis is inverted and the delay distortion is cancelled by passing the result through the cyclic filter 1' having the same characteristic as that of the cyclic filter 1 and the delay distortion is eliminated. Since the time axis is inverted, however, the cyclic filter device without delay distortion is constituted by passing the signal through the time axis inverting circuit 2' again. The cyclic filter consists of a coefficient device 3 having a coefficient (1-K), an adder 4, a delay device 5 and a coefficient device 6 having a coefficient K. Moreover, the time axis inverting circuit consists of two IH memories 7, 8, for example, when the filter is applied to a television horizontal axis, and changes over write and read operation alternately.