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Accuracy analysis of complex sinusoid amplitude and phase estimation by means of the interpolated discrete-time Fourier transform algorithm |
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| Affiliation: | 1. Faculty of Applied Mathematics and Control Processes, Saint Petersburg State University, St. Petersburg, Russia;2. Institut für Mathematik und Informatik, Universität Greifswald, Walther-Rathenau-Straße 47, Greifswald 17487, Germany;3. Université Perpignan Via Domitia, IHPE UMR 5244, CNRS, Perpignan F-66860, France;4. Theoretical Biology and Biophysics Group, Los Alamos National Laboratory, Los Alamos, New Mexico, USA |
| Abstract: | In this paper the accuracy of the complex sinusoid amplitude and phase estimators provided by the Interpolated Weighted Discrete-Time Fourier Transform (IpWDTFT) algorithm is analyzed. It is shown that the use of the WDTFT spectral sample corresponding to the estimated sinusoid frequency allows to minimize the estimator asymptotic Mean Square Error (MSE) due to additive wideband noise. Also, the expression of the asymptotic expected sum-squared fitting error in the reconstruction of the complex sinusoid by means of the IpWDTFT algorithm is derived. All the derived expressions are verified through computer simulations. |
| Keywords: | Interpolated Fourier algorithm Parameters estimation Statistical analysis Windowing |
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