Frequency de-aliased FFT analysis of step-like functions

The authors present a method for decreasing aliasing error in the fast Fourier transform (FFT) of step-like functions. This technique substantially decreases the sole remaining significant error in the extended function FFT (EF-FFT) method and is implemented by multiplying the EF-FFT spectral results with a simple de-aliasing function based on a piecewise linear model for the shape of the original function between data points. The attractive features of the aliasing error reduction method introduced, compared to increasing the sampling rate, are that data reacquisition is not required, computer requirements are small, and the spectra are of high accuracy up to the Nyquist frequency. The applicability is limited to functions that can be modeled with linear transitions between data points, as opposed to step transitions unless the precise timing and shape of the step transitions are known. Since most data sets are comprised of samples from slowly varying analog signals, the de-aliasing procedure provides enhanced spectral accuracy with minor additional mathematical complexity