Significance of autocorrelation in chemistry
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Correlation Functions are useful mathematical tools adopted in many fields of science, from engineering to physics and chemistry. Cross-Correlation function is often defined as a sliding inner (dot) product and it represents the measure of similarity of two signals as a function of a shift applied to one of them:
(1)
where and are two general non-discrete functions without discontinuity, is the complex conjugate of and is the lag (time delay for signal analysis). This representation is closely related to the convolution theorem by the following relationship:
(2)
In our case the signal must be compared with itself to find periodic patterns or anomalous high “similarity” degree within a time interval. To fulfill our purpose we can use Autocorrelation Function (ACF) wich is a simply cross-correlation of a signal with it self (). Next equation define ACF that results from a simple revaluation of equation number
(1)
where and are two general non-discrete functions without discontinuity, is the complex conjugate of and is the lag (time delay for signal analysis). This representation is closely related to the convolution theorem by the following relationship:
(2)
In our case the signal must be compared with itself to find periodic patterns or anomalous high “similarity” degree within a time interval. To fulfill our purpose we can use Autocorrelation Function (ACF) wich is a simply cross-correlation of a signal with it self (). Next equation define ACF that results from a simple revaluation of equation number
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