Fast Synthesis of Elliptic Prototype Filters

An elliptic filter features equi-ripple responses in both passband and stopband, and it has the best selectivity among prototype filters with the same degree. This letter proposes a fast iterative synthesis technique for elliptic filtering functions based on the observation that elliptic functions are special cases of generalized Chebyshev functions. After elliptic filtering functions are obtained, coupling matrix techniques can be applied to synthesize elliptic filters in the cascaded dual extracted-pole (DEP) form, which can be further transformed into the classical ladder prototype network.