On The Uniqueness Of Sparse Time-frequency Representation Of Multiscale Data

With the development of human civilization and the progress of science and technology,the world has entered the era of big data.However,the data is time-sensitive,and the data is produced at a particularly fast speed,which requires you to handle it very quickly.If you can not handle it on time,the data will be out of date.Therefore,it is more and more important to develop effective data analysis tools to extract useful information from massive data.Frequency is one of the most important features for oscillatory data.In many physical problems,frequencies encode important information of the underlying physical mechanism,so the time-frequency analysis in data analysis tool is more important.This article will be divided into there chapters.The first chapter mainly includes the foreword,the research status of time-frequency analysis,the research content and the research idea.In the second chapter,we analyze the uniqueness of the sparse timefrequency decomposition.That is under the assumption of scale separation,we show that the sparse time-frequency decomposition is unique up to an error that is determined by the scale separation property of the signal.In the third chapter,we investigate the efficiency of the nonlinear matching pursuit method and further show that the unique decomposition can be obtained approximately by the sparse time-frequency decomposition using nonlinear matching pursuit.