The ringing effects due to the sharp cut-offs in the ideal filter and to get rid of ringing effects, elimination of sharp cut-offs is necessary. This exactly happens in butterworth low pass filters. The transfer function of the butterworth low pass filter of order n and the cut off frequency at a distance D0 from the origin is defined as

$$H(u, v) = \dfrac1{1+[D(u, v)/D0]^2n} ................(1)$$

D(u,v) is the distance from the point (u,v) to the origin of the frequency rectangle for an M x N image. H(u,v) is the Fourier transform to the filtering mask.

Unlike the ILPF, the BLPF does not have sharp discontinuities and hence there are no ringing effects present when a BLPF is used. But as the order of the filter goes on increasing, a small amount of ringing effects does not creep in because the butterworth low pass filter tends to be an ideal filter.