Smith and Cummins 



PITCH 



Fig. 5 - Test record from pitch experiment 



least twice the highest frequency, f, in the signal [6]. Further, the recovery of 

 the original signal from the digital data is predicated on the use of an ideal filter. 



When dealing with empirical data and actual filters, this sampling theorem 

 is of little use, as there is rarely an absolute limiting frequency, F, and filters 

 cannot be built which are capable of cutting off perfectly above any assigned F . 

 It is certain that data collected from a vibrating towing-carriage does not meet 

 this condition. 



As in a practical case there are many additional considerations, such as 

 the effects of filtering on the desired signal, aliasing, interpolation methods 

 used for signal recovery, and limited availability of computer time, the selec- 

 tion of a sampling rate required to provide 1 percent accuracy is anything but 

 clear-cut. A more rigorous method of using the sampling theorem has long 

 been needed but the mathematics for anything other than the ideal case is quite 

 complex. Likewise, the obvious solution of increasing the sampling rate by 

 orders of magnitude, while within the capabilities of the analog-digital converter, 

 quickly becomes impractical from the standpoint of the increasing computer 

 time necessary for each analysis. 



In order to select the proper sampling rate, an experiment was run in which 

 typical samples of analog data were first digitized at 6,000 samples per channel 

 per second. A harmonic analysis was performed and the complex spectra so 

 obtained were used as analysis accuracy standards. The same data was then 

 sampled and analyzed at successfully lower sampling rates until a difference 

 approaching 1 percent was observed in the spectra. The sampling rate finally 

 selected was 125 samples per channel per second. This sampling rate, coupled 

 with an average run length of 48 seconds, produces approximately 6,000 data 

 points per channel per test condition, or approximately 60,000 data points per 

 test run. 



In performing the actual Fourier transformation to obtain the complex fre- 

 quency response function, an additional problem must be considered. When 



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