138 BELL SYSTEM TECHNICAL JOURNAL 



From the above, it is evident that the ideal form of receiver response to a 

 suddenly-impressed voltage would be a copy of the unit function shown in 

 Fig. 1, and that any deviation from this form will cause distortion. If the 

 building blocks of the curve e{l) are undistorted, the curve itself will like- 

 wise be reproduced free from distortion of wave form. Thus, the more 

 closely the indicial response can be made to approach the form of the unit 

 function, the more closely the receiver sound pressure p{t) will be a copy of 

 any arbitrary speech wave e{t). Curve 1, Fig. 3, shows the indicial response 

 of a receiver having a frequency range of 8000 cps, which comes rather close 

 to this ideal. On the other hand, the further the indicial response departs 

 from this ideal form, the more it will deviate from any impressed transient, 

 such as speech waves. Thus curve 2, Fig. 3, corresponds to a receiver of 

 narrow range, which contains resonant oscillations, and rises much later in 

 time than the other receiver. 



Conversion Formulae 



The indicial response is as fundamental in character as frequency response, 

 and may be converted into frequency and phase response if the proper in- 

 tegrations are carried out for any particular system, as follows: 



Indicial Response A{t) ^ [Frequency Rcsponsel ^ 



[_ -j- Phase Response J j t. ^ / 



where A (w) is the transfer admittance of the system. In order to carry out 

 these conversions, certain integrations must be performed, either mechani- 

 cally or theoretically. The following are conversions^ which may be used to 

 carry out this process: 



TT Jo 



sm Oil aui 



a; 



A{t) = P(0) -{-- f 9^ COS oitdoi 



T Jo OJ 



^ = f AiOsinuitdi 

 0) Jo 



QM = I [A{1) - Am^osoitdt 



CO Jo 



Where P(a;) and Q{(xi) are the real and imaginary parts of the frequency 

 reponse, A (co) is expressed in terms of pressure reponse*, while the indicial 

 response A {t) is expressed as an instantaneous sound pressure. The integra- 

 tions are difficult to carry out, but serve to show how the two systems of 



