04/27/2007

Kramarenko A.V.

The classical spectral evaluation is perceived as such well worked out and finished in its development method, that when it is inefficient in solving a specified problem, no other propositions are put forward, but to increase the realization or apply the methods of non-classical spectral analysis.

However, we must not forget that the development of digital methods of calculation of power spectrum took place at the times, when the computational power of processors was extremely small compared with the contemporary one. And the optimization of the method was carried out mainly in the field of speeding up computations and reducing the necessary number of mathematical operations. As to the efficiency of the method itself, its possibilities are virtually completely exhausted by the characteristics of the used data window.

It is quite possible that just because this the author of one of the most required monographs [1] allowed himself a paradoxical (at first sight) statement: "... the practice of implementation of the methods of spectral evaluation using the finite data sets is not a precise science: it is to a great extent based on experimental results and usually requires one or other particular compromises"».

Taking into account this particular opinion, we take the liberty to carry out an experimental verification of the methods of classical spectral evaluation (the author is mentally sound and does not suffer from megalomania, remembers Descartes and just only tries to call in question what came to hand).

Let us specify the following model for 512-dot realization in the floating point format:

frequency_discret=200.0; frequency=9.5; phase=0;

for(i=0;i<512;i++){ data*=0.0001*amplitude*sin((2.0*pi/frequency_discret)*(double)i*(frequency*1.4)+phase)+
0.01*amplitude*sin((2.0*pi/ frequency_discret)*(double)i*(frequency*2)+phase)+
0.000001*amplitude*sin((2.0*pi/ frequency_discret)*(double)i*(frequency*2.5)+phase)+
0.01*amplitude*sin((2.0*pi/ frequency_discret)*(double)i*(frequency*0.24)+phase)+
0.1*amplitude*sin((2.0*pi/ frequency_discret)*(double)i*(frequency+1)+phase)+
amplitude*sin((2.0*pi/ frequency_discret)*(double)i*frequency+phase);
}*

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