A novel method for dominant oscillation estimation and harmony quantification through spectral leakage suppression

Abstract

Several methods exist for the quantification of the underlying oscillation within a time series in terms of frequency, amplitude and phase. The evaluation of the discrete Fourier transform is limited to integer periods and therefore prone to spectral leakage. Other approaches detect the dominant oscillation on a continuous frequency range, but lead to a nonlinear optimization problem, resulting in high requirements for the solving algorithm. We propose a novel direct method for the quantification of the dominant oscillation based on a characteristic value – called “DOH” – which is defined both in frequency and time domain. This enables the assessment of the harmony and periodicity and is discussed for different signal-to-noise ratios and the number of periods. By iteratively calculating the DOH for a successive truncated time series, the method – called “LSDOH” – is extended to a high frequency resolution. The algorithm suppresses spectral leakage, though it does not require any windowing. The method is compared to the DFT based on a Monte Carlo simulation. It is shown that the proposed identification method is highly accurate in determining the oscillation parameters of a time series overlaid by different noise levels, especially for high sampling frequencies.