Parametric Modeling Power Spectral Estimation Based On The Linear Canonical Transform

The technology of random signal analysis and processing is widely used in many important applications.In practical applications,random signal usually cannot be described by a function of time and continuous infinitely.Therefore,we can determine the spectral content of random signal,as power spectral estimation.The methods for power spectral estimation of a stationary random signal based on Fourier transform(FT)are mainly divided into two categories: one is classical spectral estimation(non-parametric methods)based on the filtering theory,the other is the modern spectral estimation(parametric techniques)which root in time series analysis and approximation theory.The parametric modeling estimation methods allow one to replace the spectral estimation problem by a parameter estimation problem with the advantages of real-time,effective,and high-resolution.With the development of information science and technology,the movement character of things and background environment are becoming more and more complex which lead the information carried by signas presents non-stationary.Many signal processing theories and methods besed on the FT have shown a lot of limitations in dealing with non-stationary signal.As the generalization of the FT and the fractional Fourier transform(FRFT),the linear canonical transform(LCT)is more flexible for analyzing and processing non-stationary signals due to its extra three degrees of freedom comparing to the FRFT with one extra degree of freedom and the FT without any parameter.Compared to the FRFT,the LCT not only can be seen as a rotation but also an affine transform of the signal in the time-frequency plane,which makes the LCT has been gradually applied in many fields of nonstationary signal processing such as radar,sonar and communication systems.According to the linear canonical power spectrum,the linear canonical statistical characteristics of a nonstationary random signal could be represented alternatively by either the linear canonical power spectral density or the linear canonical correlation.However,both of them are proposed based on non-parametric descriptions,and thus have the shortcomings such as poor resolution or rigorous constraint.Based on the LCT fundamental theories,this paper describes a method of how to estimate the linear canonical power spectrum of the nonstationary random signal by means of parametric techniques.