On the design of digital filters as a sum of two all-pass filters

The necessary and sufficient conditions are given for a digital filter transfer function to be implementable as a sum of two all-pass filters. The conditions are derived directly in the
z
-plane. The class of filters satisfying these conditions is shown to be wider than the class of filters obtained via the bilinear transformation from the corresponding conventional analog filters. An example shows that the given conditions enable us to design complementary filter pairs with different numerator and denominator orders directly using magnitude squared functions. These filters compare favorably with the corresponding classical filters.