(difference frequency) may pass through the filter. 



Examination of the term representing the difference frequency in 

 Equation [A-A] shows that the amplitude of the lower sideband is pro- 

 portional to the amplitude of the modulating signal (A ) because 



m A = k A . To generalize to the random signal, consider that a 

 a c am 



given carrier frequency will mix with all the components in the random 

 signal, but only that component which produces a lower sideband (difference 

 frequency) of 97,000 cps will pass through the filter. 



It should be noted that filters are not as narrow as suggested here 

 so that a 5-cps filter, for example, will be centered at 97,000 cps but 

 will permit all difference frequencies between 96,997.5 cps and 97,002.5 

 cps to pass. The analog computer squares and averages all these frequencies 

 and assigns this estimate of the spectral density to the appropriate 03 

 designated by the oscillator which generates the carrier frequency. As 

 long as the spectrum is relatively flat in this area, the estimate is good. 



To summarize then, the random signal modulates a particular carrier 

 signal in such a way that only the resulting difference frequencies pass 

 through a narrow band fixed filter. The amplitudes of the passed components 

 are proportional to the amplitudes of the modulating components and the 

 frequencies are related to the carrier wave. If the carrier wave frequency 

 is constantly increased, all the frequencies in the random signal may be 

 identified. After a component is passed through the filter, it is sent to 

 an analog computer where it is squared, and then to an X-Y plotter where 

 the squared amplitude- voltage is displayed against frequency. Adjust- 

 ment of the ordinate and abscissa scale to account for transducer and 



analyzer calibrations results in a plot of spectral density versus frequency, 



32 



