148 BELL SYSTEM TECHNICAL JOURNAL 



Figure 8 shows a group of curves of the frequency response and indicial re- 

 sponse of a group of receivers used as hearing aids. Curve 1 shows a very 

 efficient but resonant receiver. Curve 2 is somewhat damped but still 

 contains oscillations. Curve 3 is comparatively much better than either 

 of the others from an indicial response viewpoint, and has a drooping fre- 

 quency response characteristic, and demonstrates the advantages of this 

 form of curve. 



Figure 9 shows the effect of adding damping to the system of the string 

 oscillograph when subjected to an ideal square wave. Curve 1, which has 

 a virtually flat characteristic from 1 to 10,000 cps, is characterized by a 

 sharp oscillatory peak in the indicial response. Curve 2 contains some oscil- 

 lations, while curve 3 is substantially free from oscillations. The trend of 

 these curves also shows the more faithful reproduction of transients obtained 

 with a drooping frequency response. 



Figure 10 shows the response to square waves of three receivers having 

 different frequency response characteristics. The low-frequency waves of 50 

 cps are similar to the indicial response of the three receivers whose frequency 

 characteristics are shown at the top, Fig. 10. As the frequency of these 

 waves is increased to 300 cps, a noticeable departure from the square form 

 is apparent in receiver No. 3. Receiver No. 2 shows a slight departure, 

 while No. 1 is virtually a perfect reproduction. 



As the frequency of the square waves is increased to 500 cps, the receiver 

 No. 1 still shows very Httle departure from the original form. Receiver No. 

 2 maintains a fair approximation, while receiver No. 3 has lost all resem- 

 blance to the square form. 



At a frequency of 1000 cps, only the first receiver maintains an approxi- 

 mately square form. Receivers Nos. 2 and 3 have both lost their identity 

 and have become practically pure sinusoids. For all higher frequencies of 

 the square waves, these two receivers will exhibit practically pure sinusoidal 

 forms, due to the relatively sloping character of the frequency response at 

 these frequencies, and the absence of harmonics. The same will be true of 

 receiver No. 1 beyond a frequency of 3000 cps. 



It will be realized, of course, that the patterns were obtained with square 

 waves repeated at frequencies of 50, 300, 500 and 1000 cycles per second. 

 While some speech waves approximate square waves in character such 

 waves, when they occur, are repetitive only at the lower range of these fre- 

 quencies. The above patterns were therefore obtained under conditions 

 much more severe than are involved in the reproduction of speech waves and 

 are included primarily for the purpose of illustrating the sensitivity of this 

 form of analysis when applied to repeated square waves. 



