THE CORRELATOGRAPH 



1183 



term correlation gives a mottled background level. The signal pattern 

 shows through this background quite plainly when the two powers are 

 equal. As the signal is reduced relative to the noise the signal pattern is 

 obscured and seems entirely missing at 20 db below the noise level. This 

 is a limitation based mainly on the integration time of this particular 

 apparatus. It is possible to improve the resolution by using longer in- 

 tegration periods with corresponding sacrifice of ability to detect fast 

 changes in the applied signal. As pointed out by C. B. Feldman, the 

 autocorrelation type of analysis suffers the same sort of limitations in the 

 low signal-to-noise ratio case as filtering after detection imposes in 

 spectral analysis. That is, finite integration time in the autocorrelation 

 case and finite filter band width in the postdetection filter both allow 

 errors from interaction of noise with noise to swamp the relatively small 

 desired effect of signal.* Cross-correlation on the other hand is like filter- 

 ing ahead of the detector in that the interaction of noise with noise is 

 suppressed leaving as the dominant error the relatively small interac- 

 tion of noise with signal. We cannot obtain this advantage of cross- 

 correlation if we do not have available a noisefree signal to cross-correlate 

 with, and analogously an accurate knowledge of the frequency to be 

 selected is helpful in securing the best possible results from predetection 

 filtering. 



It Avill be noted that alternate stripes of the signal pattern fade at 

 first as the signal is decreased relative to the noise. This effect appears 

 to be associated with incomplete suppression by the multiplier of the 

 components proportional to the squares of the individual noise inputs. 

 If the noise inputs were steady, the squares would produce mainly direct 

 current which is not transmitted by the product amplifier. Variation in 



Fig. 7 — Correlatograiii of single-frequency wave. 



* The autocorrelation method however has an advantage if the signal can be 

 recognized at all in that it is capable of measuring the frequency of the original 

 components, which the postdetection filter cannot do at best. 



