Formulas for parameter scaling in the McClellan transform

In using the original 1-D to 2-D McClellan transform , scaling of the transform parameters [4,5] is necessary to guarantee that . In a recent letter [7], we have presented extremely simple formulas for the scaling factors, then proposed a modified transform which not only is scaling-free but also contains one fewer parameter than the original transform. The work in [7] however is restricted only to common elliptical isopotential contours. In this paper, we analyse the problem for more general cases.