Spectral Estimation Of Random Signals And Its Improvements

The power spectral density has been widely used in many fields, from which we can know how the power is distributed over frequency. Spectrum estimation is to use the data of limited length to estimate the power spectrum of the signal. It can be divided into classical and modern spectrum estimation. However, with the improvement of science, spectrum estimation is requested to improve. In addition, the multidimensional random signal plays a more and more important role in the practice. Multidimensional spectrum estimation is a challenging problem.The classical and modern spectrum estimations are briefly discussed firstly. The essence of classical spectrum estimation is the traditional Fourier transform. Modern spectrum estimation is based on the parameter model. When the length of data is short, the resolution of classic spectrum estimation is low and the variance is large. Modern spectrum estimation is proposed based on the disadvantages of classical spectrum estimation. But it also has disadvantages:the selection of model order is difficult and so on.Secondly, this paper introduces the THREE spectrum estimation based on Kullback-Leibler distance and Hellinger distance. We propose an alternative iter-ative algorithm to solve the Lagrange multiplier in the convex optimization prob-lem. Based on spectrum estimation of one dimension random signal, the THREE spectrum estimation is extended to the spectrum estimation of multidimension-al random signal. The estimation hinges on the best approximation of a given spectral density with respect to a distance between spectral density functions.At last, the simulations are designed to confirm the algorithms. Simulations show that the resolution is higher at the specific frequency. It performs well when the length of data is short. And we also demonstrate the superiority of THREE spectrum estimation, which is more reliable and can effectively detect spectral lines and steep variations compared with other methods.