Equiripple approximation based on a rotating unit vector
Donald Allen Rudberg · Montana State University ScholarWorks (Montana State University) · 1966
A transformation, first presented by Bennett in 1952, leading to equiripple lowpass magnitude squared functions is re-examined.It is cast in the form of a complex rotating unit vector.Bandpass and high-pass generating functions leading to magnitude squared functions follow immediately when considered as rotating vectors.Pole locations are arbitrary.Modifications provide general equiripple rational, function with and without symmetry about the origin.The method is shown to be well adapted to formation of equiripple passband and, stopband functions by iterative procedures.Any lengths of passband and stopband can be accomodated.Limitations of the method are pointed out.: Numerous examples are included, both single band functions with arbitrary poles and equiripple passband and stopband functions.The method is recommended to students,and practicing engineers as either, a complement to or substitute for the elliptic function approach.