90
A. A. Minda et al.
varying the signal length, the spectral lines are not anymore distributed equidistantly,
so the sinc function cannot be used as interpolation support.
It was also found that, for any frequency, the errors are small enough to permit
an accurate frequency estimation if the signal has a sufficiently length, i.e., a large
number of cycles. Based on our expertize, we recommended to consider at least 25
cycles of the targeted frequency, in which case the error becomes less than 1%.
We have also found that the pseudo-sinc function follows a polynomial function
of 5th degree and have shown that the coefficients for any frequency can be derived
if the coefficients for another frequency are known.
The practical use of the proposed pseudo-sinc function consists in the support
to estimate the true amplitude and frequency from measured signals, with direct
application in vibration-based damage assessment.
References
1. D. Belega, D. Dallet, D. Petri, Accuracy of sine wave frequency estimation by multipoint
interpolated DFT approach. IEEE Trans. Instrum. Meas. 59(11), 2808–2815 (2010)
2. T. Grandke, Interpolation algorithms for discrete Fourier transforms of weighted signals. IEEE
Trans. Instrum. Meas. 32, 350–355 (1983)
3. B.G. Quinn, Estimating frequency by interpolation using Fourier coefficients. IEEE Trans. Sig.
Process. 42, 1264–1268 (1994)
4. V.K. Jain, W.L. Collins, D.C. Davis, High-accuracy analog measurements via interpolated FFT.
IEEE Trans. Instrum. Meas. 28, 113–122 (1979)
5. K. Ding, C. Zheng, Z. Yang, Frequency estimation accuracy analysis and improvement of
energy barycenter correction method for discrete spectrum. J. Mech. Eng. 46(5), 43–48 (2010)
6. P. Voglewede, Parabola approximation for peak determination. Glob. DSP Mag. 3(5), 13–17
(2004)
7. E. Jacobsen, P. Kootsookos, Fast, accurate frequency estimators. IEEE Sig. Process. Mag.
24(3), 123–125 (2007)
8. J.L. Ntakpe, G.R. Gillich, I.C. Mituletu, Z.I. Praisach, N. Gillich, An accurate frequency estimation algorithm with application in modal analysis. Rom. J. Acoust. Vib. 13(2), 98–103
(2016)
9. K. Duda, Interpolation algorithms of DFT for parameters estimation of sinusoidal and damped
sinusoidal signals, in Fourier Transform-Signal Processing (2012), pp. 1–32
10. G.R. Gillich, P.F. Minda, Z.I. Praisach, A.A. Minda, Natural frequencies of damaged beams—a
new approach. Rom. J. Acoust. Vib. 9(2), 101–108 (2012)
11. G.R. Gillich, A.A. Minda, Z.I. Korka, Precise estimation of the resonant frequencies of
mechanical structures involving a pseudo-sinc based technique. J. Eng. Sci. Innov. 2(4), 37–48
(2017)
A. A. Minda et al.
varying the signal length, the spectral lines are not anymore distributed equidistantly,
so the sinc function cannot be used as interpolation support.
It was also found that, for any frequency, the errors are small enough to permit
an accurate frequency estimation if the signal has a sufficiently length, i.e., a large
number of cycles. Based on our expertize, we recommended to consider at least 25
cycles of the targeted frequency, in which case the error becomes less than 1%.
We have also found that the pseudo-sinc function follows a polynomial function
of 5th degree and have shown that the coefficients for any frequency can be derived
if the coefficients for another frequency are known.
The practical use of the proposed pseudo-sinc function consists in the support
to estimate the true amplitude and frequency from measured signals, with direct
application in vibration-based damage assessment.
References
1. D. Belega, D. Dallet, D. Petri, Accuracy of sine wave frequency estimation by multipoint
interpolated DFT approach. IEEE Trans. Instrum. Meas. 59(11), 2808–2815 (2010)
2. T. Grandke, Interpolation algorithms for discrete Fourier transforms of weighted signals. IEEE
Trans. Instrum. Meas. 32, 350–355 (1983)
3. B.G. Quinn, Estimating frequency by interpolation using Fourier coefficients. IEEE Trans. Sig.
Process. 42, 1264–1268 (1994)
4. V.K. Jain, W.L. Collins, D.C. Davis, High-accuracy analog measurements via interpolated FFT.
IEEE Trans. Instrum. Meas. 28, 113–122 (1979)
5. K. Ding, C. Zheng, Z. Yang, Frequency estimation accuracy analysis and improvement of
energy barycenter correction method for discrete spectrum. J. Mech. Eng. 46(5), 43–48 (2010)
6. P. Voglewede, Parabola approximation for peak determination. Glob. DSP Mag. 3(5), 13–17
(2004)
7. E. Jacobsen, P. Kootsookos, Fast, accurate frequency estimators. IEEE Sig. Process. Mag.
24(3), 123–125 (2007)
8. J.L. Ntakpe, G.R. Gillich, I.C. Mituletu, Z.I. Praisach, N. Gillich, An accurate frequency estimation algorithm with application in modal analysis. Rom. J. Acoust. Vib. 13(2), 98–103
(2016)
9. K. Duda, Interpolation algorithms of DFT for parameters estimation of sinusoidal and damped
sinusoidal signals, in Fourier Transform-Signal Processing (2012), pp. 1–32
10. G.R. Gillich, P.F. Minda, Z.I. Praisach, A.A. Minda, Natural frequencies of damaged beams—a
new approach. Rom. J. Acoust. Vib. 9(2), 101–108 (2012)
11. G.R. Gillich, A.A. Minda, Z.I. Korka, Precise estimation of the resonant frequencies of
mechanical structures involving a pseudo-sinc based technique. J. Eng. Sci. Innov. 2(4), 37–48
(2017)