Efficacy of the frequency and damping estimation of a real-value sinusoid Part 44 in a series of tutorials on instrumentation and measurement

Sinusoidal and damped sinusoidal signals are common in different branches of engineering. Estimation of frequency and damping is very important in many fields [1]–[15], e.g., linear system identification, speech processing, image processing, transient analysis, electric power system analysis, radar and sonar systems, communication, nuclear magnetic resonance spectroscopy (NMRS), mechanical spectroscopy, economics, seismology, and others. The literature on the subject is very rich. Recently an interesting introduction to frequency and damping estimation methods was published in the IEEE Instrumentation & Measurement Magazine [15]. In this paper, we focus on the methods with the best performance for a single component, damped, real-valued sinusoidal signal disturbed by additive white Gaussian noise. In our previous works [14] and [16]–[18], we investigated these estimation methods, two-point and three-point interpolated Discrete Fourier Transform (IpDFT) for an undamped sinusoidal signal analyzed with Rife-Vincent class I, Kaiser-Bessel and Dolph-Chebyshev windows, methods of Bertocco, Yoshida and Bertocco-Yoshida family for orders 0-3, the Agrez algorithm, IpDFT for damped sinusoidal signal analyzed with Rife-Vincent class I windows, time domain and frequency domain Least Squares (LS) optimization, Hilbert transform, covariance, Prony, iterative Steiglitz-McBride (STMB), Kumaresan-Tufts, total least squares, Matrix Pencil (MatPen), and Pisarenko. For this presentation, we choose only the best methods from the above set, i.e. the Bertocco-Yoshida order 1 (BY1) STMB and MatPen. We also describe the iterative leakage correction algorithm [19] with application to BY1, and compare all results with the well-known Aboutanios and Mulgrew algorithm (AbM) [13]. Our intention is to describe and compare the best existing algorithms. We consider a real-valued signal because it is a typical measurement case. The DFT spectrum of this signal is disturbed by a spectral leakage [5].