The command
rgd( <order> , <ripple> ) ;generates a ripple-group-delay filter of order <order>. The parameter <ripple> is the group-delay ripple in seconds. The resulting filter is a low-pass filter. Its bandwidth in which it approximates a constant group delay within the ripple specification is 1rad/s.
Like Bessel filters, ripple-group-delay filters approximate constant group delay in their pass bands. While the Bessel filter has zero group-delay ripple, the ripple-group-delay filter has a specified non-zero amount of ripple. Allowing this ripple has the advantage that the stop-band damping increases.
As an example, figure 1 shows the group-delay respones of a fifth-order ripple-group-delay filter with one second ripple generated with the command rgd(5,1); with the response of a fifth-order Bessel filter with the same amount of group-delay variation in the band between zero and 1rad/s. Figure 2 compares the damping characteristics of these filters. It is clearly visible that the ripple-group-delay filter has a larger amount of stop-band damping.
