Research On Signal Decomposition Algorithm And Application Based On Amplitude Modulated And Frequency Modulated Model

Most of the signals obtained from nature or artificial systems(such as biomedical engineering,mechanical vibration systems,speech recognition systems,etc.)are complex multi-component signals.In order to facilitate the analysis and processing of signals,it is often necessary to decompose the signals into the form of the sum of some simple signals.With the wide application of signal processing technology in mobile communication,medical detection and consumer electronics,many new requirements are put forward for signal decomposition and representation.Therefore,the decomposition and representation of complex signals is an important research topic in signal processing.Since the 1960 s,with the continuous improvement and enrichment of information technology theory,many signal decomposition frameworks have been put forward.Especially in the past ten years,a large number of model-based signal decomposition algorithms have been proposed and applied to engineering experiments.Empirical mode decomposition algorithm,variational mode decomposition algorithm,dynamic Chirp model decomposition algorithm and so on all belong to the model driven signal optimization decomposition algorithm,these algorithms can effectively extract the specific model components in the signal.Although these algorithms have achieved some results in the field of signal decomposition,the above algorithms have some limitations,which are mainly reflected in the imperfect generality of the signal model and the limited estimation accuracy of the model.In addition,these algorithms can not accurately estimate the model parameters when dealing with spectrum cross aliasing.Based on time-frequency analysis,a signal decomposition algorithm based on amplitude modulated and frequency modulated(AMFM)model is proposed.The main research and innovation of this thesis are as follows:(1)Based on a large number of scientific experiments,the AMFM models of real and complex domains are deeply studied,and the corresponding AMFM mathematical expression models are established.This thesis provides a theoretical basis for the study of model-based signal decomposition algorithm.(2)On the basis of the AMFM model,the signal decomposition algorithm of the single complex AMFM model is proposed.The convex optimization equation of the signal model is established by estimating the instantaneous frequency of the model,and the parameters of the model are estimated by the convex optimization solution and the partial differential equation solution.In the process of solving the optimization equation,the parameters such as Lagrangian coefficient and leakage factor are introduced,and the optimization iteration formula of the optimization parameters is put forward,and the convergence of the algorithm is proved.Programming to implement the algorithm,and through testing experiments to verify the effectiveness of the algorithm.(3)Based on the single model signal decomposition algorithm,a signal decomposition algorithm for multi-multiple AMFM model is proposed.At the beginning of the signal decomposition algorithm based on the AMFM model,the signal is extracted one by one through the model,each extraction makes the extracted component and the residual component meet the optimization constraint,but when there is a frequency cross component,the algorithm is difficult to satisfy the global optimization constraint.Therefore,we propose a signal decomposition algorithm based on multiple complex AMFM model.Convex optimization equations of multi-models in complex domain are constructed based on the single model signal decomposition algorithm,the model components are extracted by optimization solution and partial differential solution,and the parameters such as instantaneous amplitude and instantaneous frequency of the model are accurately estimated.To study the effect of optimization parameters on the performance of the algorithm and to derive the optimization iterative formula of the parameters.The algorithm is programmed and verified by simulation data and measured data.(4)Multi-model signal decomposition algorithm for real number domain is proposed.The multi-model signal decomposition algorithm in complex domain needs to obtain the analytic formula of the signal by Hilbert transformation.This operation requires that the signal must conform to the Bedrosian theorem and be easily affected by noise and other factors.In this thesis,the multi-model optimization algorithm of complex domain is solved by using Euler formula and matrix block method,and the multi-model optimization algorithm of real domain is derived.Studying the correlation between the complex domain AMFM model and the real domain model,the optimization equation of signal decomposition algorithm based on real domain AMFM model is derived by using Euler formula and matrix block solution method,and the optimization iterative formula of solving parameters is obtained.Implementation of the algorithm through code,and through experiments to verify the real-domain multi-model signal decomposition algorithm feasibility and stability.