Search

This paper develops a new frame for non-stationary signal separation, which is a combination of wavelet transform, clustering strategy and local maximum approximation. We provide a rigorous mathematical theoretical analysis and prove that the proposed algorithm can estimate instantaneous frequencies and sub-signal modes from a blind source signal. The error bounds for instantaneous frequency estimation and sub-signal recovery are provided. Numerical experiments on synthetic and real data demonstrate the effectiveness and efficiency of the proposed algorithm. Our method based on wavelet transform can be extended to other time–frequency transforms, which provides a new perspective of time–frequency analysis tools in solving the non-stationary signal separation problem. [ABSTRACT FROM AUTHOR]

Analyzing and breaking down nonstationary signals into their primary components is significant in various optical applications. In this work, we design a direct, localized, and mathematically rigorous method for nonstationary signals by employing a modulated short-time Fourier transform (MSTFT) that can be implemented efficiently using fast Fourier transform, subsequently isolating energy-concentrated sets through an approximate threshold process, allowing us to directly retrieve instantaneous frequencies and signal components by determining the maximum frequency within each set. MSTFT provides a new insight into the time-frequency analysis in multicomponent signal separation and can be extended to other time-frequency transforms. Beyond the analysis of the synthetic, we also perform real dual-comb ranging signals under turbid water, and the results show an approximate 1.5 dB improvement in peak signal-to-noise ratio, further demonstrating the effectiveness of our method in challenging conditions. [ABSTRACT FROM AUTHOR]

Model selection and parameter estimation are very important in many fields. However, the existing methods have many problems, such as low efficiency in model selection and inaccuracy in parameter estimation. In this study, we proposed a new algorithm named improved approximate Bayesian computation sequential Monte Carlo algorithm (IABC-SMC) based on approximate Bayesian computation sequential Monte Carlo algorithm (ABC-SMC). Using the IABC-SMC algorithm, given data and the set of two models including logistic and Gompertz models of infectious diseases, we obtained the best fitting model and the values of unknown parameters of the corresponding model. The simulation results showed that the IABC-SMC algorithm can quickly and accurately select a model that best matches the corresponding epidemic data among multiple candidate models and estimate the values of unknown parameters of model very accurately. We further compared the effects of IABC-SMC algorithm with that of ABC-SMC algorithm. Simulations showed that the IABC-SMC algorithm can improve the accuracy of estimated parameter values and the speed of model selection and also avoid the shortage of ABC-SMC algorithm. This study suggests that the IABC-SMC algorithm can be seen as a promising method for model selection and parameter estimation. [ABSTRACT FROM AUTHOR]