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New form of the Fourier transform for time-varying frequency estimation

Show simple item record Katkovnik Vladimir en 2012-11-01T16:31:40Z 2012-11-01T16:31:40Z 1995 en
dc.identifier.citation Conference Proceedings of the International Symposium on Signals, Systems and Electronics en
dc.description.abstract The local polynomial Fourier transform (LPFT) and the local polynomial periodogram (LPP) are proposed in order to estimate the rapidly time-varying instantaneous frequency (IF) Ω(t) of a harmonic signal. The LPFT gives the time-frequency power distribution over the t - (Ω(t), dΩ(t)/dt, ..., dm-1Ω(t)/dtm-1) space, where m is a degree of the LPFT. The LPFT enables one to estimate both the time-varying frequency and its derivatives. The technique is based on fitting the local polynomial approximation of the frequency which implements a high-order nonparametric regression. The a priori information about bounds for the frequency and its derivatives can be incorporated to improve the accuracy of the estimation. The asymptotic mean square errors, bias and covariance, of the estimators of dsΩ(t)/dts, s = 0, 1, 2,..., m - 1, are obtained. The considered estimators are high-order generalization of the short-time Fourier transform. The comparative study of the asymptotic variance and bias of the estimates is presented. en
dc.language.iso en en
dc.publisher IEEE, Piscataway, NJ, United States en
dc.subject Approximation theory; Errors; Estimation; Fourier transforms; Polynomials; Spectrum analysis; Asymptotic variance; Local polynomial Fourier transform; Local polynomial periodogram; Time varying instantaneous frequency; Signal theory en
dc.title New form of the Fourier transform for time-varying frequency estimation en
dc.type Conference Paper en

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