Truncations and phase relationships of sinusoids
Philip L. Jackson · Journal of Geophysical Research Atmospheres · 1967
Fourier transforms of severely truncated sinusoids have recently been computed digitally by Toman [1965]. He found that maximums seldom occur at the frequency of the sinusoid. Toman's experiments showed that among other frequency anomalies a 1-cps sine wave with zero initial phase shows a maximum in the Fourier transform at approximately 0.84 cps when evaluated at a truncation length of 1 sec. My purpose is to discuss the basis of the frequency shift anomalies which Toman's experiment revealed and to generalize the results for other initial phases.