Uncertainty Relation in Analytical Chemistry

It has been shown that the application of the de-convolution method will result in a significant information gain in problems of analytical chemistry. 

Therefore, we raise the question how much the selectivity can be improved by using such methods. We may also formulate the problem, as we ask how much more 

We illustrate the basic restriction of such methods with an example. The Fourier transform of a sine wave gives the delta function. To obtain the delta function, in fact, we must integrate over a time interval from —oo to +oo. If over finite time interval a wave train is integrated, then in the Fourier transform contributions of other frequencies creep in that are not there originally in fact. This is known as the classical uncertainty relation. 

The same is true for problems related to analytical chemistry. In order to compress the response of a chemical compound to an infinite small range in the spectral density function, in the spectrum the data in the infinite range of wave numbers must be known. Or in the case of a chromatogram, it must be sampled over an infinite range of time. In this case, basically an infinite number of compounds could be separated. If only the measurement in a finite domain is possible, then basically only a finite amount of compounds can be separated. However, the consideration is still limited by the fact that the measurement of the peaks, etc., is not possible to a limited accuracy. In practice, the latter objection seems to be even more restrictive. 

On differential equations with periodic integrals. Ann. Math. 3(5), 145-153 (1887) 

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