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The instantaneous frequency (IF) is a very important feature of nonstationary signals in numerous applications. The first overview of the concept and application of the IF estimators is presented in seminal papers by Boashash. Since then, a significant knowledge has been gained about the performance of the IF estimators. This knowledge has been used not only for development of various IF estimators but also for introduction of novel time–frequency (TF) representations. The IF estimation in environments characterized by low signal-to-noise (SNR) has achieved significant benefits from these theoretical developments. In this paper, we review some of the most important developments in the last two decades related to the concept of the IF, performance analysis of IF estimators, and development of IF estimators for low SNR environments. [ABSTRACT FROM AUTHOR]

For wideband array signals, existing self-calibration methods use a first order approximation to simplify the estimation procedure under the assumption of small sensor position errors. However, the performance will degrade severely as the position errors increase. In this paper, a novel self-calibration method based on the time-frequency distributions (TFDs) is proposed to relieve the small errors constraint. We firstly develop an approach for wideband signals to select the TFDs of each source. Then the TFDs are utilized to obtain the propagation delays, which have a simple linear relationship with the sensor positions. The direction of arrival (DOA) and positions are finally estimated by a two-step iteration without any approximation. Simulation results demonstrate that the proposed method can achieve accurate DOA and position estimation over a broad range of position errors with lower computational complexity, and outperforms existing self-calibration algorithms. [ABSTRACT FROM AUTHOR]

The aim of this paper is to improve the energy concentration of the Stockwell transform (S-transform) in the time–frequency domain. A modified S-transform is proposed with several parameters to control the width of a hybrid Gaussian window. A constrained optimization problem is proposed based on an energy concentration measure as objective function and inequalities constraints to define the bounds of the Gaussian window. An active-set algorithm is applied to resolve the optimization problem. The optimization of the energy concentration in the time–frequency plane can lead to more reliable applications for non-stationary signals. The simulation results show a significant improvement of the proposed methodology most notably in the presence of noise comparing with the standard S-transform and existing modified S-transform in the literature. Moreover, comparison with other known time–frequency transforms such as Short-time Fourier transform (STFT) and smoothed-pseudo Wigner–Ville distribution (SPWVD) is also performed and discussed. The proposed S-transform is tested also on real non-stationary signals through an example of split detection in heart sounds. [ABSTRACT FROM AUTHOR]

Model-based adaptive signal decomposition algorithm is an important research topic in the field of signal analysis. The amplitude modulated and frequency modulated (AM-FM) model is the most common model in the signal. In this paper, an adaptive signal decomposition algorithm based on the complex AM-FM model is proposed. This algorithm first obtains the analytical expression of the analyzed signal; and then the optimal equation of the analytic signal based on the model is realized by initializing the instantaneous frequency (IF) of the model. Finally, the partial differential equation and the alternating direction method of multipliers technique are used to solve the optimization equation to achieve a high precision estimation of the model. Experiments on simulated and real-life data verify that the proposed algorithm can accurately estimate the instantaneous amplitude (IA) and IF of each component in the signal, and has strong robustness and high efficiency. [ABSTRACT FROM AUTHOR]