Sine-wave Frequency Estimation Research Articles

Prior Rough Estimation and Trigonometric Decomposition Method for Frequency Estimation of Sine Wave Distorted by Noise

Frequency estimation of sine wave distorted by noise plays an important role in modern power systems. The widely used windowed interpolation fast Fourier transform (WIFFT) can only reduce, but not completely remove, the estimation errors at the cost of an increment in the computation burden of frequency estimation. This paper proposes a frequency estimator by using the prior rough frequency estimation and trigonometric decomposition under white Gaussian noises. Firstly, a prior rough frequency is estimated by the three spectral lines WIFFT based on the Hanning window. Then, a parallel iteration of trigonometric decomposition is applied for the accurate frequency estimation. The gradient-descent method is used in the parallel iteration procedure, which can effectively restrain the interferences from harmonics and noise. Simulation and experiments results show that the proposed method can achieve accurate frequency estimation within one cycle.

Power System Frequency Estimation of Sine-Wave Corrupted With Noise by Windowed Three-Point Interpolated DFT

This paper presents a symmetric three points IpDFT (S3IpDFT) method which can be associated with all combined cosine windows. The influence of spectral interference from image component and noise on the power system frequency estimation provided by the S3IpDFT is investigated. The expression for the absolute error of the normalized frequency caused by the spectral interference from image component is presented. Also, the analytical expression of the frequency estimation variance has been derived. The derived results are validated by means of computer simulations and experiments.

Comparison of sine-wave frequency estimation methods in respect of speed and accuracy for a few observed cycles distorted by noise and harmonics

Comparison of sine-wave frequency estimation methods in respect of speed and accuracy for a few observed cycles distorted by noise and harmonics

Effect of noise and harmonics on sine-wave frequency estimation by interpolated DFT algorithms based on few observed cycles

In this paper the performances of two state-of-the-art Interpolated Discrete Fourier Transform (IpDFT) algorithms are analyzed when sine-wave frequency must be estimated over short observation intervals. The first estimator, called enhanced IpDFT (e-IpDFT) algorithm, exploits a two-point interpolation and compensates the detrimental contribution of the fundamental image component on the estimated frequency by using an iterative procedure. The second estimator, called IpDFT-EIF algorithm, eliminates that contribution by using a three-point interpolation. Both algorithms reduce the spectral leakage due to time-domain truncation by weighting the acquired signal by a Maximum Sidelobe Decay (MSD) window. The analysis is performed in the case of ideal, noisy, and noisy and harmonically distorted sine-waves. Theoretical expressions for the estimation Mean Square Errors (MSEs) due to noise and harmonics are derived and verified through simulations and experiments. The performed analysis allows the selection of the best frequency estimator for given signal-to-noise-ratio, harmonic content, and number of acquired cycles.

Accuracy of Sine Wave Frequency Estimation by Multipoint Interpolated DFT Approach

This paper focuses on the frequency-domain estimation of the normalized frequency of a sine wave corrupted by a stationary white noise. The weighted multipoint interpolated discrete Fourier transform method is considered, and its effect on both the spectral interference due to the image component and the additive wideband noise is taken into account. In particular, the expression of the combined standard uncertainty of the estimator is derived in the case when the H-term maximum sidelobe decay window (H ≥ 2) is used, and the number of interpolation points is 2J + 1 (J ≥ 1). Based on this expression, the number of interpolation points that minimize the estimator-combined uncertainty can be determined. The derived results are validated by means of computer simulations and applied to experimental data.