i-RheoFT: Fourier transforming sampled functions without artefacts

In this article we present a new open-access code named “i-RheoFT” that implements the analytical method first introduced in [PRE, 80, 012501 (2009)] and then enhanced in [New J Phys 14, 115032 (2012)], which allows to evaluate the Fourier transform of any generic time-dependent function that vanishes for negative times, sampled at a finite set of data points that extend over a finite range, and need not be equally spaced. I-RheoFT has been employed here to investigate three important experimental factors: (i) the ‘density of initial experimental points’ describing the sampled function, (ii) the interpolation function used to perform the “virtual oversampling” procedure introduced in [New J Phys 14, 115032 (2012)], and (iii) the detrimental effect of noises on the expected outcomes. We demonstrate that, at relatively high signal-to-noise ratios and density of initial experimental points, all three built-in MATLAB interpolation functions employed in this work (i.e., Spline, Makima and PCHIP) perform well in recovering the information embedded within the original sampled function; with the Spline function performing best. Whereas, by reducing either the number of initial data points or the signal-to-noise ratio, there exists a threshold below which all three functions perform poorly; with the worst performance given by the Spline function in both the cases and the least worst by the PCHIP function at low density of initial data points and by the Makima function at relatively low signal-to-noise ratios. We envisage that i-RheoFT will be of particular interest and use to all those studies where sampled or time-averaged functions, often defined by a discrete set of data points within a finite time-window, are exploited to gain new insights on the systems’ dynamics.