The form of these filters in two dimensions is given by
This transfer function is smooth, like Butterworth filter. Gaussian in frequency domain remains a Gaussian in spatial domain
Advantage: No ringing artifacts
Where D0 is the cutoff frequency. When D(u,v) = D0, the GLPF is down to 0.607 of its maximum value. This means that a spatial Gaussian filter, obtained by computing the IDFT of above equation., will have no ringing.
