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Discrete-time local polynomial approximation of the instantaneous frequency

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1 Author(s)
Katkovnik, V. ; Dept. of Stat., South Africa Univ., Pretoria, South Africa

The local polynomial approximation (LPA) of the time-varying phase is used to develop a new form of the Fourier transform and the local polynomial periodogram (LPP) as an estimator of the instantaneous frequency (IF) Ω(t) of a harmonic complex-valued signal. The LPP is interpreted as a time-frequency energy distribution over the t-(Ω(t), Ω1(t)),...,Ωm-1(t) space, where m is a degree of the LPA. The variance and bias of the estimate are studied for the short- and long-time asymptotic behavior of the IF estimates. In particular, it is shown that the optimal asymptotic mean squared errors of the estimates of Ωk-1(t) have orders O(N-(2k+1)) and O(N-/2(m-k+1)2m+3), k=1.2,...,m, respectively, for a polynomial Ω(t) of the degree m-1 and arbitrary smooth Ω(t) with a bounded mth derivative

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Signal Processing, IEEE Transactions on  (Volume:46 ,  Issue: 10 )