The Correlatograph 



A Machine for Continuous Display of 



Short Term Correlation 



By W. R. BENNETT 



(Manuscript received April 24, 1953) 



An analog device has been constructed which displays short term cor- 

 relation as a three-dimensional plot in which the rectangular coordinates 

 are running time and lag time and the intensity of the pattern represents 

 the correlation function. Preliminary tests on the properties of such a device 

 are reported. 



The place of the electrical spectrograph^ as a signal analyzer has be- 

 come well established in laboratory technology. It has occurred to many 

 investigators however that the spectrum is not the only property of a 

 signal which may be worthy of study, and in recent years there has been a 

 considerable interest in other features, notably the correlation functions. 

 On the basis of the accepted mathematical definitions the auto correla- 

 tion function is the Fourier cosine transform of the power spectrum and 

 in this sense would contain equivalent information presented in a differ- 

 ent form. However, the mathematical definitions apply to a very long 

 time interval and in practice we often deal with short segments of non- 

 stationary processes. The spectrograph does not evaluate the true spec- 

 trum in such cases but gives instead a spectrum-like function of fre- 

 quency which changes with the observation time. We may regard the 

 resolving filter as performing a weighted analysis in which the most 

 recent parts of the signal contribute most heavily to the instantaneous 

 response. The resulting "short term" spectrum depends on the charac- 

 teristics of the resolving filter as well as the signal, but over a useful 

 range of filtering selectivity the individual peculiarities of the signal are 

 distinguishable even though the structural background may be charac- 

 teristic of the filter. 



"Short term" correlation functions, in which the averaging interval 

 is finite, have also been investigated and show phenomena analogous to 



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