Instantaneous Frequency Estimation Using Stochastic Calculus and Bootstrapping
<p/> <p>Stochastic calculus methods are used to estimate the instantaneous frequency of a signal. The frequency is modeled as a polynomial in time. It is assumed that the phase has a Brownian-motion component. Using stochastic calculus, one is able to develop a stochastic differential eq...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2005-01-01
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| Series: | EURASIP Journal on Advances in Signal Processing |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/ASP.2005.1886 |
| _version_ | 1828858966346563584 |
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| author | Abutaleb A |
| author_facet | Abutaleb A |
| author_sort | Abutaleb A |
| collection | DOAJ |
| description | <p/> <p>Stochastic calculus methods are used to estimate the instantaneous frequency of a signal. The frequency is modeled as a polynomial in time. It is assumed that the phase has a Brownian-motion component. Using stochastic calculus, one is able to develop a stochastic differential equation that relates the observations to instantaneous frequency. Pseudo-maximum likelihood estimates are obtained through Girsanov theory and the Radon-Nikodym derivative. Bootstrapping is used to find the bias and the confidence interval of the estimates of the instantaneous frequency. An approximate expression for the Cramér-Rao lower bound is derived. An example is given, and a comparison to existing methods is provided.</p> |
| first_indexed | 2024-12-13T02:08:07Z |
| format | Article |
| id | doaj.art-c1469c36af78480db0de08b28798eebb |
| institution | Directory Open Access Journal |
| issn | 1687-6172 1687-6180 |
| language | English |
| last_indexed | 2024-12-13T02:08:07Z |
| publishDate | 2005-01-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | EURASIP Journal on Advances in Signal Processing |
| spelling | doaj.art-c1469c36af78480db0de08b28798eebb2022-12-22T00:03:05ZengSpringerOpenEURASIP Journal on Advances in Signal Processing1687-61721687-61802005-01-01200512172584Instantaneous Frequency Estimation Using Stochastic Calculus and BootstrappingAbutaleb A<p/> <p>Stochastic calculus methods are used to estimate the instantaneous frequency of a signal. The frequency is modeled as a polynomial in time. It is assumed that the phase has a Brownian-motion component. Using stochastic calculus, one is able to develop a stochastic differential equation that relates the observations to instantaneous frequency. Pseudo-maximum likelihood estimates are obtained through Girsanov theory and the Radon-Nikodym derivative. Bootstrapping is used to find the bias and the confidence interval of the estimates of the instantaneous frequency. An approximate expression for the Cramér-Rao lower bound is derived. An example is given, and a comparison to existing methods is provided.</p>http://dx.doi.org/10.1155/ASP.2005.1886bootstrappingIto calculusinstantaneous frequencytime-varying frequencyGirsanov theory |
| spellingShingle | Abutaleb A Instantaneous Frequency Estimation Using Stochastic Calculus and Bootstrapping EURASIP Journal on Advances in Signal Processing bootstrapping Ito calculus instantaneous frequency time-varying frequency Girsanov theory |
| title | Instantaneous Frequency Estimation Using Stochastic Calculus and Bootstrapping |
| title_full | Instantaneous Frequency Estimation Using Stochastic Calculus and Bootstrapping |
| title_fullStr | Instantaneous Frequency Estimation Using Stochastic Calculus and Bootstrapping |
| title_full_unstemmed | Instantaneous Frequency Estimation Using Stochastic Calculus and Bootstrapping |
| title_short | Instantaneous Frequency Estimation Using Stochastic Calculus and Bootstrapping |
| title_sort | instantaneous frequency estimation using stochastic calculus and bootstrapping |
| topic | bootstrapping Ito calculus instantaneous frequency time-varying frequency Girsanov theory |
| url | http://dx.doi.org/10.1155/ASP.2005.1886 |
| work_keys_str_mv | AT abutaleba instantaneousfrequencyestimationusingstochasticcalculusandbootstrapping |