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Abstract: This paper proposes a three-point Interpolated Discrete Fourier Transform (IpDFT) method for frequency estimation of a discrete-time sinusoidal signal. It is based on the maximum sidelobe decay (MSD) windows and is highly effective in rejecting the detrimental effect on the estimation accuracy due to the image component of the signal spectrum. This remarkable feature is achieved by using an analytical expression based on a suitable weighting of the three largest DFT spectrum samples. The proposed method provides good results when the effect of the spectral interference due to the image component dominates other estimation error sources. The accuracy of the proposed method and of other state-of-the-art methods such as the multi-point IpDFT methods and the four-parameter sine-fitting (4PSF) algorithm are compared through both computer simulations and experimental results in the case of ideal, noisy, and harmonically distorted sinusoids. A small number of acquired cycles is assumed in order to analyze situations in which the contribution from the image component interference is significant. The performed comparison shows that the proposed method outperforms the considered multi-point IpDFT methods when the Signal-to-Noise Ratio (SNR) is higher than 30 dB and the number of acquired cycles is enough small. The proposed method outperforms also the 4PSF algorithm when the frequency estimation error is dominated by harmonics rather than wideband noise. [Copyright &y& Elsevier]

Abstract: In recent years, Hilbert–Huang Transform (HHT) is widely used to analyze nonlinear and non-stationary signals in various applications, such as seismic and biomedical signal processing. In HHT, the Empirical Mode Decomposition (EMD) is the key component for decomposing natural signals into intrinsic mode functions (IMFs). Since the EMD suffers from mode-mixing problem, in which some fast intermittent signals riding on a slow-oscillating wave, the Ensemble-EMD (EEMD) is proposed to solve this problem with the aids of noise. However, the EEMD requires high computational complexity in ensemble and is unsuitable for some real-time applications, such as ultrasound systems. In this paper, intermittent signals are modeled in mathematical forms for IMF decomposition. We then propose sinusoidal-assisted EMD (SAEMD) for efficient and effective HHT computation to solve mode-mixing problems. The type I of SAEMD (SAEMD-I) is initially proposed to solve the mode-mixing problem with very low computational complexity. However, if the maximum frequency of data is unknown in some real-world applications, the SAEMD-I may encounter estimation error caused by imprecise locations of extrema. For practical data, the type II of SAEMD (SAEMD-II) is proposed to solve the sampling rate issue. Compared with the ensemble-100 EEMD, the SAEMD-II can have 11–13 times improvement in terms of computation speed in El Niño application and comparable correlation coefficient (−0.95 at IMF 8). Hence, the proposed SAEMD-II scheme is a good candidate of implementing cost-effective HHT when computational complexity and real-time data processing are of major concern. [Copyright &y& Elsevier]

This note presents a new algorithm that is designed to identify the frequency, magnitude, phase and offset of a biased sinusoidal signal. The structure of the algorithm includes an orthogonal system generator based on a second-order generalized integrator. The proposed strategy has the advantages of a fast and accurate signal reconstruction capability and a good rejection to noise. [ABSTRACT FROM PUBLISHER]