Accurate Frequency Estimation Based On Three-Parameter Sine-Fitting With Three FFT Samples
This paper presents a simple DFT-based golden section searching algorithm (DGSSA) for the single tone frequency estimation. Because of truncation and discreteness in signal samples, Fast Fourier Transform (FFT) and Discrete Fourier Transform (DFT) are inevitable to cause the spectrum leakage and fen...
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| Format: | Article |
| Language: | English |
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Polish Academy of Sciences
2015-09-01
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| Series: | Metrology and Measurement Systems |
| Subjects: | |
| Online Access: | http://www.degruyter.com/view/j/mms.2015.22.issue-3/mms-2015-0032/mms-2015-0032.xml?format=INT |
| _version_ | 1818409835746557952 |
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| author | Liu Xin Ren Yongfeng Chu Chengqun Fang Wei |
| author_facet | Liu Xin Ren Yongfeng Chu Chengqun Fang Wei |
| author_sort | Liu Xin |
| collection | DOAJ |
| description | This paper presents a simple DFT-based golden section searching algorithm (DGSSA) for the single tone frequency estimation. Because of truncation and discreteness in signal samples, Fast Fourier Transform (FFT) and Discrete Fourier Transform (DFT) are inevitable to cause the spectrum leakage and fence effect which lead to a low estimation accuracy. This method can improve the estimation accuracy under conditions of a low signal-to-noise ratio (SNR) and a low resolution. This method firstly uses three FFT samples to determine the frequency searching scope, then – besides the frequency – the estimated values of amplitude, phase and dc component are obtained by minimizing the least square (LS) fitting error of three-parameter sine fitting. By setting reasonable stop conditions or the number of iterations, the accurate frequency estimation can be realized. The accuracy of this method, when applied to observed single-tone sinusoid samples corrupted by white Gaussian noise, is investigated by different methods with respect to the unbiased Cramer-Rao Low Bound (CRLB). The simulation results show that the root mean square error (RMSE) of the frequency estimation curve is consistent with the tendency of CRLB as SNR increases, even in the case of a small number of samples. The average RMSE of the frequency estimation is less than 1.5 times the CRLB with SNR = 20 dB and N = 512. |
| first_indexed | 2024-12-14T10:05:57Z |
| format | Article |
| id | doaj.art-18237085e2ea44249c47117149d4510a |
| institution | Directory Open Access Journal |
| issn | 2300-1941 |
| language | English |
| last_indexed | 2024-12-14T10:05:57Z |
| publishDate | 2015-09-01 |
| publisher | Polish Academy of Sciences |
| record_format | Article |
| series | Metrology and Measurement Systems |
| spelling | doaj.art-18237085e2ea44249c47117149d4510a2022-12-21T23:07:08ZengPolish Academy of SciencesMetrology and Measurement Systems2300-19412015-09-0122340341610.1515/mms-2015-0032mms-2015-0032Accurate Frequency Estimation Based On Three-Parameter Sine-Fitting With Three FFT SamplesLiu Xin0Ren Yongfeng1Chu Chengqun2Fang Wei31) North University of China, National Key Laboratory for Electronic Measurement and Technology, Taiyuan, 030051, China1) North University of China, National Key Laboratory for Electronic Measurement and Technology, Taiyuan, 030051, China1) North University of China, National Key Laboratory for Electronic Measurement and Technology, Taiyuan, 030051, China1) North University of China, National Key Laboratory for Electronic Measurement and Technology, Taiyuan, 030051, ChinaThis paper presents a simple DFT-based golden section searching algorithm (DGSSA) for the single tone frequency estimation. Because of truncation and discreteness in signal samples, Fast Fourier Transform (FFT) and Discrete Fourier Transform (DFT) are inevitable to cause the spectrum leakage and fence effect which lead to a low estimation accuracy. This method can improve the estimation accuracy under conditions of a low signal-to-noise ratio (SNR) and a low resolution. This method firstly uses three FFT samples to determine the frequency searching scope, then – besides the frequency – the estimated values of amplitude, phase and dc component are obtained by minimizing the least square (LS) fitting error of three-parameter sine fitting. By setting reasonable stop conditions or the number of iterations, the accurate frequency estimation can be realized. The accuracy of this method, when applied to observed single-tone sinusoid samples corrupted by white Gaussian noise, is investigated by different methods with respect to the unbiased Cramer-Rao Low Bound (CRLB). The simulation results show that the root mean square error (RMSE) of the frequency estimation curve is consistent with the tendency of CRLB as SNR increases, even in the case of a small number of samples. The average RMSE of the frequency estimation is less than 1.5 times the CRLB with SNR = 20 dB and N = 512.http://www.degruyter.com/view/j/mms.2015.22.issue-3/mms-2015-0032/mms-2015-0032.xml?format=INTfrequency estimationCRLBthree-parameter sine-fittingRMSEgolden section |
| spellingShingle | Liu Xin Ren Yongfeng Chu Chengqun Fang Wei Accurate Frequency Estimation Based On Three-Parameter Sine-Fitting With Three FFT Samples Metrology and Measurement Systems frequency estimation CRLB three-parameter sine-fitting RMSE golden section |
| title | Accurate Frequency Estimation Based On Three-Parameter Sine-Fitting With Three FFT Samples |
| title_full | Accurate Frequency Estimation Based On Three-Parameter Sine-Fitting With Three FFT Samples |
| title_fullStr | Accurate Frequency Estimation Based On Three-Parameter Sine-Fitting With Three FFT Samples |
| title_full_unstemmed | Accurate Frequency Estimation Based On Three-Parameter Sine-Fitting With Three FFT Samples |
| title_short | Accurate Frequency Estimation Based On Three-Parameter Sine-Fitting With Three FFT Samples |
| title_sort | accurate frequency estimation based on three parameter sine fitting with three fft samples |
| topic | frequency estimation CRLB three-parameter sine-fitting RMSE golden section |
| url | http://www.degruyter.com/view/j/mms.2015.22.issue-3/mms-2015-0032/mms-2015-0032.xml?format=INT |
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