Statistical description of the sine-wave frequency estimator provided by the interpolated DFT method

This paper describes the effect of the spectral interference and wideband noise on the accuracy of the sine-wave frequency estimator provided by the Interpolated Discrete Fourier Transform (IpDFT) method based on some commonly used cosine windows. It is shown that the spectral interference contribution from the image component has a sinusoidal behaviour with respect to the sine-wave phase and the expression for its amplitude is derived. Also, a simple expression for the variance of noise contribution is derived. Based on the achieved results, the Probability Density Function (PDF) of the sine-wave frequency estimator is obtained. The accuracy of each expression derived in the paper is verified by means of computer simulations. Furthermore, the accuracy of the PDF of the sine-wave frequency estimator is verified by means of experimental results.     

Method, algorithm and device for estimation of components above the harmonic frequency range up to 9 kHz

The paper presents a method of estimation of frequency groups with 200 Hz bandwidth in the frequency range from the 50th harmonic up to 9 kHz. The method consists of the application of a fast Fourier transform (FFT) for wavelet coefficients after input signal decomposition and partial synthesis for chosen frequency bands. It enables the computational complexity of the algorithm to be reduced and also attenuates influence of the fundamental component and low-frequency harmonics, as required by IEC Standard 61000-4-7. The particulars of this method are shown and analysis for a chosen wavelet family is provided. Further, the algorithm and its implementation in real device for power quality monitoring is presented. Finally, the results of measurements of two testing signals are shown. The required attenuation of fundamental component and required accuracy was obtained.     

Accuracy analysis of the normalized frequency estimation of a discrete-time sine-wave by the average-based interpolated DFT method

The normalized frequency of a sine-wave can be estimated by the average of the two estimates achieved using the Interpolated Discrete Fourier Transform (IpDFT) method. This approach is called average-based IpDFT method. The paper investigates the effect of the spectral interference from the image component and additive wideband noise on the accuracy of the normalized frequency estimator provided by the average-based IpDFT method with maximum sidelobe decay windows in the case of a discrete-time sine-wave. The expressions of the maximum of the normalized frequency estimator error due to the spectral interference and variance of the normalized frequency estimator due to the wideband noise are derived. Also, the expression of the combined standard uncertainty of the normalized frequency estimator is derived. The accuracies of all derived expressions are confirmed by means of computer simulations. Moreover, the performance of the average-based IpDFT method is compared with those of a state-of-the-art three-point IpDFT method and IpDFT method through both computer simulations and experimental results.