Transfer functions with poles located on parabolic and elliptic contours

Polynomial transfer functions with parabolic and elliptic distribution of poles, which have been studied previously by Mullick and Scanlan, are derived from the Butterworth unit circle by suitable conformal mappings. Transient responses of the filters with elliptic distribution of poles for orders n=3¿6 have been calculated and compared with those of parabolic and catenary filters.