Combination of Two Discrete Fourier Transforms of Data Sampled Separately at Different Rates

This paper is motivated by a demand for increasing the frequency-resolution in power spectrum analysis using ordinary data-acquisition-equipment, even if the speeds of sampling and quantization is so moderate as to yield confusion between the low and high frequencies. For this purpose, in our proposal, a given record is sampled separately at slightly different rates, e.g., T/2N and T/2(N-n) seconds respectively for every period T second, where 1≤n≤N. From these time-series of samples, two Fourier coefficients are computed separately by the usual Discrete Fourier Transform (DFT). To improve this effect, the two discrete Fourier coefficients are combined. By solving simple algebraic equations of the corresponding order-coefficients, i.e., the frequency-components in the original record can lx distinguished from one another. The maximum frequency that can be defined in this version is [2(N-n)-1]/T Hz, not more than two times as high as that anticipated by a single version of the usual DFT. This algorithm has instant effects not only on improving the frequency-resolution, but on damping the socalled Gibbs phenomenon near discontinuous points of a reconstructed rectangular wave.