Fourier analyses are made on two functions. The first is a step function forward from periodic samples of a sinusoid. If the frequency of the sinusoid is less than one-half of the sampling frequency, it is shown that the step function has no frequency components less than one-half of the sampling frequency other than that of phase, and duration with respect to the interval of the analysis. It is shown that the insertion of a blank space in the period of analysis reduces greatly the uncertainty of the amplitude of the initial sinusoid as estimated from the results of the Fourier analysis. The results of the analyses are useful in the design and evaluation of certain analog data-analyzing systems.