Frequency estimation from proper sets of correlations
As a complement to the periodogram, low-complexity frequency estimators are of interest. One such estimator is based on Prony's method and rely on phase information of the auto correlations. Without prior knowledge of the frequency (e.g., a given frequency interval), the frequency cannot be una...
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| Published in | IEEE transactions on signal processing Vol. 50; no. 4; pp. 791 - 802 |
|---|---|
| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
New York, NY
IEEE
01.04.2002
Institute of Electrical and Electronics Engineers The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
| Subjects | |
| Online Access | Get full text |
| ISSN | 1053-587X 1941-0476 1941-0476 |
| DOI | 10.1109/78.992122 |
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| Abstract | As a complement to the periodogram, low-complexity frequency estimators are of interest. One such estimator is based on Prony's method and rely on phase information of the auto correlations. Without prior knowledge of the frequency (e.g., a given frequency interval), the frequency cannot be unambiguously estimated from a single correlation only. We introduce a new method of phase unwrapping using an arbitrary number (more than one) of correlations. From this arbitrary set of correlations, we propose a weighted average estimator. We derive the asymptotic performance and show how the correlation lags should be properly chosen. From a design aspect, there is often a restriction of using a fixed number of computations. In addition, we therefore propose a strategy to find a proper set of correlation lags subject to a given computational complexity. Finally, simulation results that lend support to the theoretical findings are included. |
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| AbstractList | As a complement to the periodogram, low-complexity frequency estimators are of interest. One such estimator is based on Prony's method and rely on phase information of the auto correlations. Without prior knowledge of the frequency (e.g., a given frequency interval), the frequency cannot be unambiguously estimated from a single correlation only. In this paper, we introduce a new method of phase unwrapping using an arbitrary number (more than one) of correlations. From this arbitrary set of correlations, we propose a weighted average estimator. We derive the asymptotic performance and show how the correlation lags should be properly chosen. From a design aspect, there is often a restriction of using a fixed number of computations. In addition, we therefore propose a strategy to find a proper set of correlation lags subject to a given computational complexity. Finally, simulation results that lend support to the theoretical findings are included. As a complement to the periodogram, low-complexity frequency estimators are of interest. One such estimator is based on Prony's method and rely on phase information of the auto correlations. Without prior knowledge of the frequency (e.g., a given frequency interval), the frequency cannot be unambiguously estimated from a single correlation only. We introduce a new method of phase unwrapping using an arbitrary number (more than one) of correlations. From this arbitrary set of correlations, we propose a weighted average estimator. We derive the asymptotic performance and show how the correlation lags should be properly chosen. From a design aspect, there is often a restriction of using a fixed number of computations. In addition, we therefore propose a strategy to find a proper set of correlation lags subject to a given computational complexity. Finally, simulation results that lend support to the theoretical findings are included As a complement to the periodogram, low-complexity frequency estimators are of interest. One such estimator is based on Prony's method and rely on phase information of the auto correlations. Without prior knowledge of the frequency (e.g., a given frequency interval), the frequency cannot be unambiguously estimated from a single correlation only. We introduce a new method of phase unwrapping using an arbitrary number (more than one) of correlations. From this arbitrary set of correlations, we propose a weighted average estimator. We derive the asymptotic performance and show how the correlation lags should be properly chosen. From a design aspect, there is often a restriction of using a fixed number of computations. In addition, we therefore propose a strategy to find a proper set of correlation lags subject to a given computational complexity. Finally, simulation results that lend support to the theoretical findings are included. |
| Author | Handel, P. Volker, B. |
| Author_xml | – sequence: 1 givenname: B. surname: Volker fullname: Volker, B. organization: Dept. of Signals, Sensors, & Syst., R. Inst. of Technol., Stockholm, Sweden – sequence: 2 givenname: P. surname: Handel fullname: Handel, P. |
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| Keywords | Performance evaluation Parameter estimation Phase unwrapping Simulation Signal estimation Frequency estimation Computational complexity Correlation method Periodogram Prony method |
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| SubjectTerms | Applied sciences Asymptotic properties Autocorrelation Automotive components Background noise Complement Computation Computational complexity Computational modeling Computer simulation Correlation Detection, estimation, filtering, equalization, prediction Estimators Exact sciences and technology Frequency estimation Geophysical measurements Geophysical signal processing Information, signal and communications theory low complexity optimization Phase estimation phase unwrapping Radar applications Radar signal processing Signal and communications theory Signal, noise single-frequency Strategy Telecommunications and information theory threshold |
| Title | Frequency estimation from proper sets of correlations |
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