Transfer Functions with Elliptic Distribution of Poles at Equal Frequency Spacings

This paper presents the amplitude and phase-delay responses for a class of transfer functions with all zeros at infinity and poles located on an ellipse in the complex frequency plane, with equal spacings along the imaginary axis. The class is generated by varying the eccentricity of the ellipse, and it is found that when the ratio of the axis in the real direction to that in the imaginary direction lies in the range 0.4-0.8, good delay responses result, together with wide amplitude bandwidths. By varying the eccentricity in the range mentioned, a choice of amplitude and delay response can be made to facilitate any particular application.