Reducing noise in computed correlation functions using techniques from signal processing

Time correlation functions invariably suffer from random noise, especially at longer time intervals for which fewer data pairs are available. This noise is particularly of concern when calculating correlations that cannot be averaged over per-molecule contributions, such as stress in molecular simulations. In this work, a set of methods based in signal processing has been developed to reduce the inherent noise that is present in time- and frequency-domain representations of correlation functions. The stress time autocorrelation function, which leads to stress relaxation modulus and complex modulus, is used as an example. The difference between initial and final values of a time correlation function over a finite time domain is found to create so-called ‘leakage’ of noise from disallowed into harmonic frequencies during fast Fourier transformation. Decreasing this leakage effect through reflection to negative time and through applying a window function reduces noise levels significantly. Removing frequency components of insignificant magnitudes also provides significant noise reduction. Applying moving averages in the frequency and time domains also contributes to noise reduction. Specific results obtained by applying these methods to a model asphalt system enable more clear physical interpretations of the underlying relaxations after dramatic noise level reductions were attained.