An efficient algorithm for frequency estimation from cosine-sum windowed DFT coefficients
•A numerically efficient method for frequency estimation by Interpolation on DFT coefficients.•The use of generic cosine-sum windows for interference suppression.•Performance that nearly achieves the Cramer–Rao bounds. This paper presents an algorithm for estimating frequency of a complex sinusoid f...
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| Published in | Signal processing Vol. 166; p. 107245 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier B.V
01.01.2020
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| Subjects | |
| Online Access | Get full text |
| ISSN | 0165-1684 1872-7557 |
| DOI | 10.1016/j.sigpro.2019.107245 |
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| Abstract | •A numerically efficient method for frequency estimation by Interpolation on DFT coefficients.•The use of generic cosine-sum windows for interference suppression.•Performance that nearly achieves the Cramer–Rao bounds.
This paper presents an algorithm for estimating frequency of a complex sinusoid from three DFT coefficients. In particular, we consider the case where the signal is multiplied by a generic cosine-sum window for interference suppression. The algorithm is an interpolator that uses the peak sample in the DFT of the data and its two neighbors. The interpolator is based on a numerically efficient procedure which guarantees convergence to a solution. Performance of the proposed interpolator is shown to be nearly optimum and comparable to the best interpolator in the literature, while the computational burden required for the proposed algorithm is much lower than the generic numerical methods available. Degradation of performance due to interference is also investigated. |
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| AbstractList | •A numerically efficient method for frequency estimation by Interpolation on DFT coefficients.•The use of generic cosine-sum windows for interference suppression.•Performance that nearly achieves the Cramer–Rao bounds.
This paper presents an algorithm for estimating frequency of a complex sinusoid from three DFT coefficients. In particular, we consider the case where the signal is multiplied by a generic cosine-sum window for interference suppression. The algorithm is an interpolator that uses the peak sample in the DFT of the data and its two neighbors. The interpolator is based on a numerically efficient procedure which guarantees convergence to a solution. Performance of the proposed interpolator is shown to be nearly optimum and comparable to the best interpolator in the literature, while the computational burden required for the proposed algorithm is much lower than the generic numerical methods available. Degradation of performance due to interference is also investigated. |
| ArticleNumber | 107245 |
| Author | Kwak, Chulhyun Kim, Gwangtae Shin, Donghoon |
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| Keywords | Interpolation Cosine-sum windows Frequency estimation Discrete Fourier transform Complex sinusoid |
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| References | Liao, Chen (bib0005) 2014; 94 Belega, Petri (bib0012) 2015; 117 Nielsen (bib0007) 1991 Belega, Dallet, Petri (bib0010) 2010; 59 Duda, Magalas, Majewski, Zielinski (bib0011) 2011; 60 Andria, Savino, Trotta (bib0009) 1989; 38 Aboutanios (bib0003) 2005; 53 Candan (bib0014) 2015; 114 Kay (bib0001) 1993 Macleod (bib0002) 1998; 46 Nocedal, Wright (bib0016) 2006 Candan (bib0004) 2013; 20 Press, Teukolsky, Vetterling, Flannery (bib0015) 2002 Rife, Vincent (bib0006) 1970; 49 Agrez (bib0008) 2002; 51 Duda (bib0013) 2011; 60 Nocedal (10.1016/j.sigpro.2019.107245_bib0016) 2006 Liao (10.1016/j.sigpro.2019.107245_bib0005) 2014; 94 Rife (10.1016/j.sigpro.2019.107245_bib0006) 1970; 49 Aboutanios (10.1016/j.sigpro.2019.107245_bib0003) 2005; 53 Candan (10.1016/j.sigpro.2019.107245_bib0004) 2013; 20 Belega (10.1016/j.sigpro.2019.107245_bib0012) 2015; 117 Kay (10.1016/j.sigpro.2019.107245_bib0001) 1993 Duda (10.1016/j.sigpro.2019.107245_bib0011) 2011; 60 Andria (10.1016/j.sigpro.2019.107245_bib0009) 1989; 38 Belega (10.1016/j.sigpro.2019.107245_bib0010) 2010; 59 Duda (10.1016/j.sigpro.2019.107245_bib0013) 2011; 60 Press (10.1016/j.sigpro.2019.107245_bib0015) 2002 Candan (10.1016/j.sigpro.2019.107245_bib0014) 2015; 114 Macleod (10.1016/j.sigpro.2019.107245_bib0002) 1998; 46 Agrez (10.1016/j.sigpro.2019.107245_bib0008) 2002; 51 Nielsen (10.1016/j.sigpro.2019.107245_bib0007) 1991 |
| References_xml | – volume: 114 start-page: 245 year: 2015 end-page: 250 ident: bib0014 article-title: Fine resolution frequency estimation from three DFT samples: case of windowed data publication-title: Signal Process. – volume: 49 start-page: 197 year: 1970 end-page: 228 ident: bib0006 article-title: Use of the discrete fourier transform in the measurement of frequencies and levels of tones publication-title: Bell Syst. Tech. J. – volume: 46 start-page: 141 year: 1998 end-page: 148 ident: bib0002 article-title: Fast nearly ML estimation of the parameters of real or complex single tones or resolved multiple tones, publication-title: IEEE Trans. Signal Process. – volume: 53 start-page: 1237 year: 2005 end-page: 1242 ident: bib0003 article-title: Iterative frequency estimation by interpolation on fourier coefficients, publication-title: IEEE Trans. Signal Process. – volume: 38 start-page: 856 year: 1989 end-page: 863 ident: bib0009 article-title: Windows and interpolation algorithms to improve electrical measurement accuracy, publication-title: IEEE Trans. Instrum. Meas. – volume: 60 start-page: 3608 year: 2011 end-page: 3618 ident: bib0011 article-title: DFT-based estimation of damped oscillation parameters in low-frequency mechanical spectroscopy publication-title: IEEE Trans. Instrum. Meas. – year: 2006 ident: bib0016 article-title: Numerical Optimization publication-title: Science and Business Media, LLC, 233 Spring Street, NY 10013 – volume: 59 start-page: 2808 year: 2010 end-page: 2815 ident: bib0010 article-title: Accuracy of sine wave frequency estimation by multipoint interpolated DFT approach, publication-title: IEEE Trans. Instrum. Meas. – volume: 20 start-page: 913 year: 2013 end-page: 916 ident: bib0004 article-title: Analysis and further improvement of fine resolution frequency estimation method from three DFT samples, publication-title: IEEE Signal Process. Lett. – volume: 60 start-page: 3608 year: 2011 end-page: 3618 ident: bib0013 article-title: DFT interpolation algorithm for Kaiser–Bessel and Dolph–Chebyshev windows publication-title: IEEE Trans. Instrum. Meas. – year: 1991 ident: bib0007 article-title: Sonar Signal Processing – volume: 117 start-page: 115 year: 2015 end-page: 125 ident: bib0012 article-title: Frequency estimation by two- or three-point interpolated, fourier algorithm based on cosine windows publication-title: Signal Process. – year: 1993 ident: bib0001 article-title: Fundamentals of Statistical Signal Processing: Estimation Theory – year: 2002 ident: bib0015 article-title: Numerical recipes in c - the art of scientific computing publication-title: The Pitt Building, Trumpington Street, Cambridge CB2 1RP – volume: 94 start-page: 108 year: 2014 end-page: 117 ident: bib0005 article-title: Phase correction of discrete fourier transform coefficients to reduce frequency estimation bias of single tone complex sinusoid, publication-title: Signal Process. – volume: 51 start-page: 287 year: 2002 end-page: 292 ident: bib0008 article-title: Weighted multipoint interpolated DFT to improve amplitude estimation of multifrequency signal, publication-title: IEEE Trans. Instrum. Meas. – year: 1993 ident: 10.1016/j.sigpro.2019.107245_bib0001 – year: 2002 ident: 10.1016/j.sigpro.2019.107245_bib0015 article-title: Numerical recipes in c - the art of scientific computing – volume: 51 start-page: 287 issue: 2 year: 2002 ident: 10.1016/j.sigpro.2019.107245_bib0008 article-title: Weighted multipoint interpolated DFT to improve amplitude estimation of multifrequency signal, publication-title: IEEE Trans. Instrum. Meas. doi: 10.1109/19.997826 – volume: 46 start-page: 141 issue: 1 year: 1998 ident: 10.1016/j.sigpro.2019.107245_bib0002 article-title: Fast nearly ML estimation of the parameters of real or complex single tones or resolved multiple tones, publication-title: IEEE Trans. Signal Process. doi: 10.1109/78.651200 – volume: 60 start-page: 3608 issue: 11 year: 2011 ident: 10.1016/j.sigpro.2019.107245_bib0011 article-title: DFT-based estimation of damped oscillation parameters in low-frequency mechanical spectroscopy publication-title: IEEE Trans. Instrum. Meas. doi: 10.1109/TIM.2011.2113124 – volume: 59 start-page: 2808 issue: 11 year: 2010 ident: 10.1016/j.sigpro.2019.107245_bib0010 article-title: Accuracy of sine wave frequency estimation by multipoint interpolated DFT approach, publication-title: IEEE Trans. Instrum. Meas. doi: 10.1109/TIM.2010.2060870 – volume: 49 start-page: 197 issue: 2 year: 1970 ident: 10.1016/j.sigpro.2019.107245_bib0006 article-title: Use of the discrete fourier transform in the measurement of frequencies and levels of tones publication-title: Bell Syst. Tech. J. doi: 10.1002/j.1538-7305.1970.tb01766.x – volume: 38 start-page: 856 issue: 4 year: 1989 ident: 10.1016/j.sigpro.2019.107245_bib0009 article-title: Windows and interpolation algorithms to improve electrical measurement accuracy, publication-title: IEEE Trans. Instrum. Meas. doi: 10.1109/19.31004 – volume: 60 start-page: 3608 issue: 3 year: 2011 ident: 10.1016/j.sigpro.2019.107245_bib0013 article-title: DFT interpolation algorithm for Kaiser–Bessel and Dolph–Chebyshev windows publication-title: IEEE Trans. Instrum. Meas. doi: 10.1109/TIM.2011.2113124 – volume: 53 start-page: 1237 issue: 4 year: 2005 ident: 10.1016/j.sigpro.2019.107245_bib0003 article-title: Iterative frequency estimation by interpolation on fourier coefficients, publication-title: IEEE Trans. Signal Process. doi: 10.1109/TSP.2005.843719 – volume: 20 start-page: 913 issue: 9 year: 2013 ident: 10.1016/j.sigpro.2019.107245_bib0004 article-title: Analysis and further improvement of fine resolution frequency estimation method from three DFT samples, publication-title: IEEE Signal Process. Lett. doi: 10.1109/LSP.2013.2273616 – volume: 114 start-page: 245 year: 2015 ident: 10.1016/j.sigpro.2019.107245_bib0014 article-title: Fine resolution frequency estimation from three DFT samples: case of windowed data publication-title: Signal Process. doi: 10.1016/j.sigpro.2015.03.009 – year: 1991 ident: 10.1016/j.sigpro.2019.107245_bib0007 – volume: 94 start-page: 108 year: 2014 ident: 10.1016/j.sigpro.2019.107245_bib0005 article-title: Phase correction of discrete fourier transform coefficients to reduce frequency estimation bias of single tone complex sinusoid, publication-title: Signal Process. doi: 10.1016/j.sigpro.2013.05.021 – year: 2006 ident: 10.1016/j.sigpro.2019.107245_bib0016 article-title: Numerical Optimization – volume: 117 start-page: 115 year: 2015 ident: 10.1016/j.sigpro.2019.107245_bib0012 article-title: Frequency estimation by two- or three-point interpolated, fourier algorithm based on cosine windows publication-title: Signal Process. doi: 10.1016/j.sigpro.2015.05.005 |
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| SubjectTerms | Complex sinusoid Cosine-sum windows Discrete Fourier transform Frequency estimation Interpolation |
| Title | An efficient algorithm for frequency estimation from cosine-sum windowed DFT coefficients |
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