Improving the Accuracy of Estimates
of the Frequencies Based
on a Pseudo-sinc Function
Andrea Amalia Minda , Gilbert-Rainer Gillich , Ana-Maria Budai ,
Nicoleta Gillich , and Cristian Paul Chioncel
Abstract The methods currently used for frequency estimation do not provide accurate results as the obtained values depend on the acquisition time. To increase the
estimates’ accuracy, the authors propose a pseudo-sinc function that is dependent on
the acquisition time but better reflect the physical phenomenon. The paper provides a
new interpolation method developed to take into account more maximizer, obtained
by iteratively cropping the source signal. The maximizer obtained in this way corresponds to an asymmetric pseudo-sinc function, which does not coincide with the
assumptions generated by the commonly used interpolation methods. The method of
interpolation using the pseudo-sinc function, developed by the authors, has as a direct
practical application, the detection of changes in the mechanical characteristics of
the engineering structures.
1 Introduction
The idea of low sensitivity in frequency evaluation stems from the fact that estimating the natural frequency by standard methods is influenced by acquisition time
[1]. Advanced methods of processing the acquired signals involve the use of an interpolation algorithm. At present, the interpolation involves analyzing the maximizer
and one or two neighbor spectral lines [2–7]. Frequency estimation from one spectrum increases the precision of the results but does not solve the problem of direct
dependence on acquisition time. Another approach is cropping the signal and taking
three maximizer from three spectra obtained from the same signal after cropping [8].
To accurately evaluate the frequencies of a signal, this study proposes a technique
that involves the analysis of an overlapped spectrum composed of maximizer from
different spectra obtained from a signal analyzed for different time lengths. In this
way, the frequencies obtained become insensitive to the length of the signal and the
errors are very small compared to those recorded by the standard methods. Through
A. A. Minda (B) · G.-R. Gillich · A.-M. Budai · N. Gillich · C. P. Chioncel
Universitatea “Eftimie Murgu” Resita, 320085 Resita, Romania
e-mail: a.minda@uem.ro
© Springer Nature Switzerland AG 2021
N. Herisanu and V. Marinca (eds.), Acoustics and Vibration of Mechanical
Structures—AVMS 2019, Springer Proceedings in Physics 251,
https://doi.org/10.1007/978-3-030-54136-1_9
85
of the Frequencies Based
on a Pseudo-sinc Function
Andrea Amalia Minda , Gilbert-Rainer Gillich , Ana-Maria Budai ,
Nicoleta Gillich , and Cristian Paul Chioncel
Abstract The methods currently used for frequency estimation do not provide accurate results as the obtained values depend on the acquisition time. To increase the
estimates’ accuracy, the authors propose a pseudo-sinc function that is dependent on
the acquisition time but better reflect the physical phenomenon. The paper provides a
new interpolation method developed to take into account more maximizer, obtained
by iteratively cropping the source signal. The maximizer obtained in this way corresponds to an asymmetric pseudo-sinc function, which does not coincide with the
assumptions generated by the commonly used interpolation methods. The method of
interpolation using the pseudo-sinc function, developed by the authors, has as a direct
practical application, the detection of changes in the mechanical characteristics of
the engineering structures.
1 Introduction
The idea of low sensitivity in frequency evaluation stems from the fact that estimating the natural frequency by standard methods is influenced by acquisition time
[1]. Advanced methods of processing the acquired signals involve the use of an interpolation algorithm. At present, the interpolation involves analyzing the maximizer
and one or two neighbor spectral lines [2–7]. Frequency estimation from one spectrum increases the precision of the results but does not solve the problem of direct
dependence on acquisition time. Another approach is cropping the signal and taking
three maximizer from three spectra obtained from the same signal after cropping [8].
To accurately evaluate the frequencies of a signal, this study proposes a technique
that involves the analysis of an overlapped spectrum composed of maximizer from
different spectra obtained from a signal analyzed for different time lengths. In this
way, the frequencies obtained become insensitive to the length of the signal and the
errors are very small compared to those recorded by the standard methods. Through
A. A. Minda (B) · G.-R. Gillich · A.-M. Budai · N. Gillich · C. P. Chioncel
Universitatea “Eftimie Murgu” Resita, 320085 Resita, Romania
e-mail: a.minda@uem.ro
© Springer Nature Switzerland AG 2021
N. Herisanu and V. Marinca (eds.), Acoustics and Vibration of Mechanical
Structures—AVMS 2019, Springer Proceedings in Physics 251,
https://doi.org/10.1007/978-3-030-54136-1_9
85