Sampling Intervals in Fourier Analysis

Fourier analysis requires data taken at equally spaced intervals. If you didn't measure the data that way (e.g. if you measured them continuously or at uneven intervals), interpolate to get values at equally spaced points, for the Fourier analysis. (I'll call the interval at which basic data were originally measured the sampling interval. Some authors don't use the term in exactly that way.) The sampling interval influences the amount of detail attainable in the analysis. The shortest resolvable period is twice the sampling interval. In other words, defining any given frequency component requires at least two samples (more than two are better) per cycle. (If the sampling interval isn't small enough to identify the shortest periods that contribute significant variance to the record, the method won't lose this short-period variance but reports it as harmonics of the shortest computed period [Wastler 1963: 18].) A small sampling interval also makes possible a greater number of samples for a given length of record and gives you more confidence in the estimates of the power spectrum.