IXDICIAL RESPONSE OF TELEPHONE RECEIVERS 149 



Conclusions 



To summarize these data, it seems evident that square wave analysis may 

 be applied in some fields of acoustics for both theoretical and practical 

 applications. 



In theory, the indicial response forms a somewhat different approach to 

 the problem of obtaining the optimum characteristics of telephone receivers 

 at the upper end of the frequency range. The greatest value of the square 

 wave analysis lies in the fact that it gives us an entirely different conception 

 of the behavior of an ideal sound system in terms of the unit function. The 

 frequency response characteristic is ordinarily interpreted on the theory that 

 any transient, such as an interval of conversation, may be represented by a 

 Fourier series of sinusoidal frequencies of constant intensity lasting over the 

 entire interval. If these equivalent component frequencies are to be repro- 

 duced in their true proportions, the ideal sound system must have mathe- 

 matically uniform response for all single frequencies. On the other hand, 

 the indicial response characteristic is judged from the Carson extension 

 theorem, which shows that the more closely this characteristic approaches 

 the unit function, the more perfect will be the reproduction of any given 

 transient. Thus, the unit function and the sinusoid may be used as mutually 

 complementary tools of analysis to show different aspects of the same type 

 of problem. 



In sound systems which are not ideal, due to inherent physical limitations, 

 we tend to apply the Fourier Theorem out to a certain frequency, just as if 

 it were an ideal system out to this frequency, and then beyond this fre- 

 quency we do not attempt to sustain the higher frequencies. For most 

 faithful reproduction of transients, it would seem that such practices might 

 be altered somewhat to advantage by allowing the frequency response to 

 drop off more gradually wherever it seems feasible to do so. The exact shape 

 of the ideal curve under these circumstances is a matter of compromise 

 between excessive delay on the one hand and excessive oscillations on the 

 other. In practice, however, a fairly good picture is soon formed when 

 curves such as the last in Figs. 6, 8, and 9 are found to approach the ideal 

 more closely than those of other forms. Such listening tests as have been 

 made tend to confirm these views, but cannot be regarded as being more 

 than an indication. 



Square wave analysis is somewhat limited in its practical applications to 

 cases which may be interpreted by inspection. Systems having only a single 

 cutoff frequency, or in the case of an additional low-end cutoff, ratios of the 

 upper and lower cutoff frequencies /2//1 of 100 or more, seem necessary to 

 interpret the results by inspection. 



