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AUTHOR(S): Ahmed S. Abutaleb
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ABSTRACT The maximum likelihood method is used to estimate the frequency of the sinusoid when the frequency is described as a known stochastic process (for example Ornstein-Uhlenbeck process). We use Malliavin calculus and Ito calculus to derive expressions for the estimate of the slowly varying amplitude. The need for these estimates occurs in EEG analysis, inverse synthetic aperture radar (ISAR), amplitude modulation-frequency modulation (AM-FM) problem etc .... The observations are one sinusoid with slowly varying amplitude. The observations are described as a stochastic differential equation (SDE). |
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KEYWORDS Ito Calculus, Malliavin calculus, Time-Varying Parameters, Girsanov Theory, Ornstein-Uhlenbeck process, AM-FM estimation |
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Cite this paper Ahmed S. Abutaleb. (2025) Estimation of the Random Instantaneous Frequency with Time-Varying Amplitude Using the Maximum Likelihood and the Malliavin Calculus. International Journal of Mathematical and Computational Methods, 10, 246-259 |
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