Ogilvie 



Impulse Response 



From fiv,(r) = A(r) «/?„(t) 



Fourier Trans 

 of «(<") 



/^^/-WbK^t^V^/ 



-0.1 

 -0.1 



-20 -10 



10 20 



response function obtained as the Fourier transform of this impulse response 

 function calculated through the simultaneous equation shows just about the same 

 values as the frequency response (amplitude gain) obtained from the results of 

 spectrum analysis as is demonstrated in Fig. 14. 



The example of synthesis of y(t) from the history of x(t) using this im- 

 pulse response functions is shown in Fig. 16 which shows pretty good agreement 

 with the actual observation of y(t), whichever impulse response function is used. 



Attention should be paid on the fact, however, that an analysis in the time 

 domain by means of ^y^(r) and ^^^(t) is inferior to the analysis in the frequency 

 domain in the following reasons: 



1. The choices of At, m, and N are difficult from the statistical point of 

 view. This makes it difficult to decide on the really important part of the cor- 

 relogram to be used for analysis as that part must include enough information. 



2. The evaluation of error is not easy as in the frequency response func- 

 tion. In the frequency domain, the coherency plays a big role, and makes the 

 estimation of relative error practicable. 



We have to be very careful because of the above-mentioned defects. After these 

 points have been made clear once, however, we can utilize the method to obtain 

 the impulse response fvmction from the correlations directly and use that to 

 predict the future response. For this purpose, some special type computer 



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