The extended function fast Fourier transform (EF-FFT)

The periodicity assumption implicit in fast Fourier transform (FFT) techniques can be utilized through time-domain prealiasing to obtain the spectral components of infinite-duration time-domain reflectometry signals when they can be modeled, outside the observation window, with step and/or exponential functions. The technique is shown to be more accurate than both conventional windowing and the other FFT approaches described in the literature for analysis of steplike signals. The duality equation relating the extension functions introduced in the extended function FFT (EF-FFT) method to conventional window functions is derived. Using this relation, it is shown that signals with high-frequency content only within the observation window are best analyzed with EF-FFT methods and that signals with time-distributed spectral components (e.g., speech) are best analyzed with conventional FFT methods