Efficient and Accurate Detection and Frequency Estimation of Multiple Sinusoids
The method for detection of complex sinusoids in additive white Gaussian noise and estimation of their frequencies is proposed. It contains two stages: 1) sinusoid detection (model order estimation) and coarse frequency estimation, and 2) fine frequency estimation. The proposed method operates in th...
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| Format: | Article |
| Language: | English |
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IEEE
2019-01-01
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| Series: | IEEE Access |
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| Online Access: | https://ieeexplore.ieee.org/document/8573769/ |
| _version_ | 1818644449725513728 |
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| author | Slobodan Djukanovic Vesna Popovic-Bugarin |
| author_facet | Slobodan Djukanovic Vesna Popovic-Bugarin |
| author_sort | Slobodan Djukanovic |
| collection | DOAJ |
| description | The method for detection of complex sinusoids in additive white Gaussian noise and estimation of their frequencies is proposed. It contains two stages: 1) sinusoid detection (model order estimation) and coarse frequency estimation, and 2) fine frequency estimation. The proposed method operates in the frequency domain, i.e., it uses the discrete Fourier transform (DFT) as the main tool. Sinusoid detection is performed so that a fixed probability of false alarm is provided (Neymann–Pearson criterion). For both coarse and fine frequency estimations, the three-point periodogram maximization approach is used. Simulations are carried out for variable signal-to-noise ratio, variable frequency displacement between the sinusoids and variable offset from the frequency grid. The proposed method meets the Cramér-Rao lower bound in frequency estimation and practically does not depend on the frequency displacement except for very small displacement values. In terms of model order estimation accuracy, it outperforms the state-of-the-art approaches. The most expensive operation in the method is the calculation of the DFT. Therefore, in terms of calculation complexity, the proposed method is on par with the most efficient algorithms for multiple frequency estimations. |
| first_indexed | 2024-12-17T00:15:02Z |
| format | Article |
| id | doaj.art-d22bdadc6dd8443f851984954b958b28 |
| institution | Directory Open Access Journal |
| issn | 2169-3536 |
| language | English |
| last_indexed | 2024-12-17T00:15:02Z |
| publishDate | 2019-01-01 |
| publisher | IEEE |
| record_format | Article |
| series | IEEE Access |
| spelling | doaj.art-d22bdadc6dd8443f851984954b958b282022-12-21T22:10:43ZengIEEEIEEE Access2169-35362019-01-0171118112510.1109/ACCESS.2018.28863978573769Efficient and Accurate Detection and Frequency Estimation of Multiple SinusoidsSlobodan Djukanovic0https://orcid.org/0000-0002-1048-1878Vesna Popovic-Bugarin1Faculty of Electrical Engineering, Džordža Vašingtona bb, University of Montenegro, Podgorica, MontenegroFaculty of Electrical Engineering, Džordža Vašingtona bb, University of Montenegro, Podgorica, MontenegroThe method for detection of complex sinusoids in additive white Gaussian noise and estimation of their frequencies is proposed. It contains two stages: 1) sinusoid detection (model order estimation) and coarse frequency estimation, and 2) fine frequency estimation. The proposed method operates in the frequency domain, i.e., it uses the discrete Fourier transform (DFT) as the main tool. Sinusoid detection is performed so that a fixed probability of false alarm is provided (Neymann–Pearson criterion). For both coarse and fine frequency estimations, the three-point periodogram maximization approach is used. Simulations are carried out for variable signal-to-noise ratio, variable frequency displacement between the sinusoids and variable offset from the frequency grid. The proposed method meets the Cramér-Rao lower bound in frequency estimation and practically does not depend on the frequency displacement except for very small displacement values. In terms of model order estimation accuracy, it outperforms the state-of-the-art approaches. The most expensive operation in the method is the calculation of the DFT. Therefore, in terms of calculation complexity, the proposed method is on par with the most efficient algorithms for multiple frequency estimations.https://ieeexplore.ieee.org/document/8573769/Cramér-Rao lower bounddiscrete Fourier transformmodel order estimationmultiple frequency estimationNeymann-Pearson criterion |
| spellingShingle | Slobodan Djukanovic Vesna Popovic-Bugarin Efficient and Accurate Detection and Frequency Estimation of Multiple Sinusoids IEEE Access Cramér-Rao lower bound discrete Fourier transform model order estimation multiple frequency estimation Neymann-Pearson criterion |
| title | Efficient and Accurate Detection and Frequency Estimation of Multiple Sinusoids |
| title_full | Efficient and Accurate Detection and Frequency Estimation of Multiple Sinusoids |
| title_fullStr | Efficient and Accurate Detection and Frequency Estimation of Multiple Sinusoids |
| title_full_unstemmed | Efficient and Accurate Detection and Frequency Estimation of Multiple Sinusoids |
| title_short | Efficient and Accurate Detection and Frequency Estimation of Multiple Sinusoids |
| title_sort | efficient and accurate detection and frequency estimation of multiple sinusoids |
| topic | Cramér-Rao lower bound discrete Fourier transform model order estimation multiple frequency estimation Neymann-Pearson criterion |
| url | https://ieeexplore.ieee.org/document/8573769/ |
| work_keys_str_mv | AT slobodandjukanovic efficientandaccuratedetectionandfrequencyestimationofmultiplesinusoids AT vesnapopovicbugarin efficientandaccuratedetectionandfrequencyestimationofmultiplesinusoids |