The complex-step derivative approximation
ACM Transactions on Mathematical Software (TOMS)
Extensions of the first and second complex-step derivative approximations
Journal of Computational and Applied Mathematics
Robust time-frequency distributions with complex-lag argument
EURASIP Journal on Advances in Signal Processing - Special issue on robust processing of nonstationary signals
Time-frequency distributions with complex argument
IEEE Transactions on Signal Processing
Polynomial Wigner-Ville distributions and their relationship totime-varying higher order spectra
IEEE Transactions on Signal Processing
Design of higher order polynomial Wigner-Ville distributions
IEEE Transactions on Signal Processing
Estimation and classification of polynomial-phase signals
IEEE Transactions on Information Theory
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This paper proposes an approach for robust estimation of highly-varying nonlinear instantaneous frequency (IF) in monocomponent nonstationary signals. The proposed method is based on a lower order complex-time distribution (CTD), derived by using the idea of complex-time differentiation of the instantaneous phase. Unlike other existing TFDs in the same framework, the proposed TFD is an order-free distribution which alleviates the subtractive cancellation error in IF estimation. The approach is applied to highly nonstationary monocomponent signals. Performance of the numerical implementation is compared with three existing IF estimation methods using three simulated signals. Noise analysis is also performed to evaluate the robustness of the method in presenfdece of additive noise at signal to noise ratio (SNR) varying from -10dB to 20dB. Results show that the proposed method outperforms the other methods at lower SNR and works reasonably well for the noiseless case.