Scaled correlation

[1] This filtering-like operation has the advantages of not having to make assumptions about the sinusoidal nature of the signals.

is computed as In a detailed analysis, Nikolić et al.[1] showed that the degree to which the contributions of the slow components will be attenuated depends on three factors, the choice of the scale, the amplitude ratios between the slow and the fast component, and the differences in their oscillation frequencies.

The larger the differences in oscillation frequencies, the more efficiently will the contributions of the slow components be removed from the computed correlation coefficient.

Scaled correlation has been subsequently used to investigate synchronization hubs in the visual cortex.

[3] Scaled correlation should be in many cases preferred over signal filtering based on spectral methods.

Nikolić et al.[1] have shown that the use of Wiener–Khinchin theorem to remove slow components is inferior to results obtained by scaled correlation.

These advantages become obvious especially when the signals are non-periodic or when they consist of discrete events such as the time stamps at which neuronal action potentials have been detected.