Frequency and Damping Estimation Methods - An Overview: This overview paper presents and compares different methods traditionally used for estimating damped sinusoid parameters. Firstly, direct nonlinear least squares fitting the signal model in the time and frequency domains are described. Next, possible applications of the Hilbert transform for signal demodulation are presented. Then, a wide range of autoregressive modelling methods, valid for damped sinusoids, are discussed, in which frequency and damping are estimated from calculated signal linear self-prediction coefficients. These methods aim at solving, directly or using least squares, a matrix linear equation in which signal or its autocorrelation function samples are used. The Prony, Steiglitz-McBride, Kumaresan-Tufts, Total Least Squares, Matrix Pencil, Yule-Walker and Pisarenko methods are taken into account. Finally, the interpolated discrete Fourier transform is presented with examples of Bertocco, Yoshida, and Agrež algorithms. The Matlab codes of all the discussed methods are given. The second part of the paper presents simulation results, compared with the Cramér-Rao lower bound and commented. All tested methods are compared with respect to their accuracy (systematic errors), noise robustness, required signal length, and computational complexity.

In this paper, we analyze and compare the properties of different well-known and also new nonparametric discrete Fourier transform (DFT)-based methods for resonant frequency and logarithmic decrement estimation in application to mechanical spectroscopy. We derive a new DFT interpolation algorithm for a signal analyzed with Rife-Vincent class-I windows and also propose new formulas that extend Bertocco and Yoshida methods. We study errors of the resonant frequency and logarithmic decrement estimation in realistic conditions that include measurement noise and a zero-point drift. We also investigate the systematic errors of the estimation methods of interest. A nonlinear least squares time-domain parametric signal fitting is used to determine the boundaries of statistical efficiency in all tests.

This article presented a novel method of computing the SDFT that we call the modulated SDFT (mSDFT). The sliding discrete Fourier transform (SDFT) is a recursive algorithm that computes a DFT on a sample-by-sample basis. The accumulated errors and potential instabilities inherent in traditional SDFT algorithms are drastically reduced in the mSDFT. We removed the twiddle factor from the feedback in a traditional SDFT resonator and thus the finite precision of its representation is no longer a problem.

This paper describes the discrete Fourier transform (DFT) interpolation algorithm for arbitrary windows and its application and performance for optimal noncosine Kaiser-Bessel and Dolph-Chebyshev windows. The interpolation algorithm is based on the polynomial approximation of the window's spectrum that is computed numerically. Two- and three-point (2p and 3p) interpolations are considered. Systematic errors and noise sensitivity are analyzed for the chosen Kaiser-Bessel and Dolph-Chebyshev windows and compared with Rife-Vincent class I windows.

The IEEE Std C37.118.1(a) describes synchrophasor measurement by Phasor Measurement Unit (PMU) for the system fundamental frequency. Harmonic synchrophasor, i.e. synchrophasor measured for harmonic frequencies, is not considered in the Standard. Harmonic synchrophasor is useful for harmonic state estimation, Power Quality (PQ) monitoring, and harmonic power flow analysis. In this paper we investigate usability of the Standard basic synchrophasor estimation model for estimation of harmonic phasor up to the 50th harmonic as advised by the IEC Std 61000-4-7. For estimation of harmonic phasors an application of the flat-top FIR filter is proposed. Results for the maximally flat differentiator and the interpolated DFT are also presented, confirming the superior performance of the proposed flat-top filter approach. Harmonic phasor estimation is verified with extended tests of the IEEE Std C37.118.1(a) including steady-state and dynamic conditions with additive 60 dB noise.

This paper describes interpolated discrete Fourier transform (IpDFT) for parameter estimation of sinusoidal and damped sinusoidal signals analyzed with a sin^α(x) window. For α = 0,2,4,...sin^α(x) windows are Rife-Vincent class I (RVI) windows, for which IpDFT algorithms are known. We present a new IpDFTs for α = 1,3,5,.... The bias-variance trade-off of the proposed IpDFT fits between results offered by RVI windows, e.g., for α = 1, we get higher noise immunity than Hann (RVI order 1, α = 2) window and lower bias than rectangular (RVI order 0, α = 0) window.