DISTORTION CORRECTION 507 



From electric circuit theory, the fundamental integral equation for 

 the indicial admittance h(t) becomes 



where p replaces icj. Its solution is 

 h{t) = 0, t < T 



and 



^'(0 = ~^" = a constant, / > r; 



(103) 



whence also h'{i) = o for t 9^ t, thus satisfying (100). These results 

 hold as well for the limiting case oi B = 0, meaning t = o. 



It may be pointed out here also that the converse of the latter theorem 

 does not follow. That is, if the transducer has a uniform attenuation 

 constant and a constant resistance iterative impedance, it is not nec- 

 essary that the phase constant be proportional to frequency through- 

 out the range. This is seen from the general equations or from the 

 fact that we can alter the phase characteristic non-linearly by means 

 of phase networks having zero attenuation and a constant resistance 

 iterative impedance. 



Theorem III: A symmetrical transducer made up entirely of resist- 

 ances would have the characteristics 



A = a constant, 



B = (104) 



and 



K = a constant = R. 



Many other more complicated networks satisfying (104) are known to 

 exist, as in Section 4.1. We need not, therefore, seek further to prove 

 the possible existence of such a combination of parameters. 

 For networks in which B is not zero, but 



A = a constant 

 and (105) 



K = a constant = R, 



the transfer admittance components with respect to a terminating 

 resistance R are given as 



e~^ 

 a{w) = -^-cos B 

 K 



and (106) 



i3(co) = -^sin5. 



