DETECTION OF TWO MODULATED WAVES 7 



about the same for both except for M = m = 0.5. It is of interest to 

 observe that the interfering speech received on the straight line detector 

 is verv much less in intensity than would be the case if the strong 

 desired signal were absent, and that the variation of the amplitude of 

 this frequency with intensity of the undesired carrier is greater when 

 the desired frequency is present. We have here an analytical descrip- 

 tion of the familiar masking effect which occurs when a strong unmodu- 

 lated carrier is received simultaneously with a weak modulated signal. 

 For example, when e/E = 0.1 it can be seen from Fig. 1 that the 

 relative amplitude of the component of frequency g/lTr is 0.0063 for 

 the case of the straight line detector. If this component were un- 

 affected by the presence of the strong signal it would have an amplitude 

 proportional to em and a relative amplitude of em/EM which for the 

 values here considered is 0.1. Hence the "masking" effect is here 

 responsible for a reduction of 24 db. 



Lastly, it may be mentioned that there are in the case of the straight 

 line detector certain frequencies of small amplitude which are entirely 

 absent from the square law case. However, no frequency is shown 

 the relative amplitude of which is less than 0.01 for all four pairs of 

 values of M and m, as such frequencies are unimportant. An exception 

 is made with regard to ^ ± u. This is always less than 0.01 over the 

 range considered but is included for the sake of comparison with the 

 square law results. 



Further Coxsideratiox of Detector Output 



The second harmonic of the desired signal is of importance only in 

 the square law case. It is of the nature of a distortion which is inde- 

 pendent of the interference and may be omitted from the consideration 

 of the undesired audio frequencies which are a result of the interference. 

 From Figs. 1 to 4 it is evident that the most important interfering 

 frequencies are those of angular velocity, u, q ±n, p ± u and p ± q_ 

 ± 11, the last being of importance only in the case of the square law 

 detector. It is with these frequencies, together with that of the 

 interfering speech qjlir, that we shall be chiefly concerned. 



When the relative magnitudes of the interfering frequencies, which 

 are tabulated on page 3, are multiplied by E'^M, the resulting quantities 

 are proportional to the absolute magnitudes of these frequencies. It 

 is to be noted that the frequencies of greatest interest have absolute 

 magnitudes which are linear functions of J/ or m except {p ±q ± u)l2-ir 

 which is proportional to niM, and 21 /It which is independent of both M 

 and 7)1 and will, therefore, be unaffected by the type of modulation 

 employed at either station. In case there are several frequencies 



