Research On Harmonic Restoration In Alpha Noise Background

The problem of signal processing in the background of Alpha noise is a hotspot and frontier research problem in the field of signal processing.The problem of harmonic recovery in the Alpha noise background is one of the key research directions in the field,in sonar,communication,biomedical,channel equalization,speech Recovery,automatic control,seismic signal analysis and many other fields have a wide range of applications.For this problem,traditional research is basically based on fractional lower moments and the fractional low-order statistics method derived from it.However,with the continuous deepening of fractional low-order statistics methods and applied research,the problems of fractional low-order statistics are also gradually exposed: the non-integer-order exponential operation inherent in fractional lower-order moments,which will not only cause harmonics The phase of the wave signal is distorted,and the fractional exponent cannot be expanded in the Euclidean space.Therefore,it causes great difficulties for its application in signal processing,even the most basic signal processing such as the maximum likelihood method and the least squares method.None of the methods can be used.It is for this reason that the sample correlation operator is combined with the Multi Signal Classification Algorithm(MUSIC)and the Rotation Invariant Technology(ESPRIT)algorithm to estimate the harmonic signal frequency to break through the non-integer inherent in fractional lower order statistics.The phase distortion caused by the exponential operation of the order and the fractional index can not be expanded in the Euclidean space,which effectively improves the estimation accuracy of the harmonic signal parameters.The main work of this article is as follows:1.Based on the harmonic parameter estimation background,Cramer-Rao bound in the case of Cauchy noise is proposed and the formula is deduced.The obtained formula can be used in the field of harmonic parameter estimation based on noise.2.Applying the sample correlation function,this paper proposes a sample correlation-based subspace-minimal norm MUSIC algorithm,which overcomes the problems of large computational complexity and sensitivity to noise subspace vector estimation errors in traditional MUSIC-like algorithm parameter search.3.For the sample-based subspace-minimal-norm MUSIC algorithm,which only uses the noise subspace and does not fully utilize the feature space information,an improved MUSIC algorithm based on feature space is proposed.The algorithm fully utilizes signal subspace and noise subspace.Make the estimation more accurate.4.In order to solve the problem that traditional ESPRIT algorithms can't effectively suppress the Alpha colored noise,this paper proposes a sample-based extended ESPRIT algorithm.This algorithm not only can effectively suppress Alpha noise,but also reduces the amount of calculation and makes it more efficient than the MUSIC algorithm.It has engineering significance.5.A sample-based TLS-extended ESPRIT algorithm is proposed for the problem-based generalized ESPRIT algorithm.The algorithm further reduces the computational complexity,and the harmonic signal frequency estimation results are more accurate.