Linear phase IIR filters composed of two parallel allpass sections

A class of approximately linear phase recursive digital filters composed of two allpass sections is introduced. The passband response for these filters is equiripple with the maximum number of alternations as for elliptic filters. By slightly widening the passband region and transferring some zeros close to the poles, the poles are forced to move to locations generating an approximately linear phase in the specified passband. For this class of filters, there exists an analytic formula relating the squared-magnitude response to the passband ripple and the zero locations, making the filter optimization very fast. Several examples illustrate that, especially in narrowband applications, these filters are superior to linear-phase non-recursive filters and phase equalized elliptic filters