Multipoint interpolated DFT for sine waves in short records with DC components

Abstract

This paper provides an improved multipoint interpolated digital Fourier transform (DFT) method for the estimation of sine waves in short records, in the presence of DC components. It is based on the procedure of windowing, fast Fourier transform (FFT), and spectrum interpolation. The proposed four-point interpolation simultaneously takes into consideration the fundamental component's positive and negative frequency parts and the DC component. It is composed of two steps, the first of which gives a good estimation of the fundamental frequency, and the second step estimates the fundamental amplitude and phase and the DC component at one time by the least squares method. If the fundamental component is in such a long record that it does not overlap DC in spectrum, then the proposed four-point method degenerates into a classic three-point one. From the simulation, the proposed method works well even for sine waves whose cycles in records are as small as 1.5. Compared with IEEE Standard 1057, the proposed method not only reduces the computational burden, but also has a better estimation precision for signals with harmonics.