Abstract: In U.S. Pat. No. 3,906,199, issued to R. B. Kieburtz and K. V. Mina on Sept. 16, 1975, limit cycle noise is reduced in a second order recursive digital filter by a circuit which randomly inhibits the rounding signal in one of the digital multipliers disposed in the filter. It has been found, however, that in certain instances, this approach results in even longer transients.In accordance with the present invention, random inhibiting is constrained to instances in which limit cycle noise is reduced, by monitoring, with suitable logic circuitry, the signals present in the various feedback loops of the filter. Generally, it has been found that the inhibiting circuit should be allowed to operate only if D.sub.1 and D.sub.2 satisfy predetermined magnitude and polarity relationships, where D.sub.1 .ident. a version of the filter output signal Y(n) that is removed in time by one sample interval, and D.sub.2 .ident. a version of the filter output signal Y(n) that is removed in time by two sample intervals.