NKTWOHR SVXTIIKSIS 



661 



other characteristics may be obtained, within limits, by chaii<j;ins the 

 (leliuitious of z and z^ , in terms of p and p, (eciuations (5) and (8)). 



In all cases, the definition of TchebychefT polynomial 7\. remains 

 the same in terms of z. The interval of orthogonality remains | ^ | = 1 ; 

 and the relation between p and z is always snch that the nseful fre- 

 quency interval is the p-plane mapping of | 2 | = 1 . The relation must 

 also be such that rational functions of p may be expresscvl as products 

 of rational functions, in z and 1 z respectively, corresponding to (13), 

 (14). At the same time, the physical restrictions on network singulari- 

 ties p„ must translate into manageable restrictions on the 2-plane singu- 

 larities Za . It is restrictions such as these that limit the manageable 

 useful intervals. 



It is easy to apply the "low-pass" techniques to "high-pass" in- 

 tervals, extending from Wc , through 00 , to — oj^ . The appropriate trans- 



^c/Pa- 



c^c/Po- 



•J -0.05 - 



10 



20 



80 



90 



30 40 50 60 70 



SIN"' -^ IN DEGREES 



Fig. 13 — An example of reduction in comple.xity. 



