High-accuracy Parameter Estimation Of Extreme Signals

DFT analysis is one of important signal analysis methods in the field of signal processingbecause of its concise concept and clear physical meaning. Fourier analysis method waspublished in1820s. Its application in engineering is more and more widely with the birthand development of the computer. However, the discreteness of computer leads there are aseries of errors in Fourier analysis method which is used for engineering. Scholars in thisfield have researched the discrete spectrum correction techniques for many years, so far itis already developed into a systematic theory and technology. The investigations on thespectrum correction methods of the single-frequency signal and multi-frequency signalwhose digital frequencies are far away from each other are already mature, they can satisfymost requirements in engineering. But spectrum interference error could not be eliminatedby current spectrum correction techniques, so the dense frequency signal or extreme lowfrequency signal could not be corrected by most correction techniques. Members of ouranalysis research group have committed to the investigation on the discrete spectrum errorfor many years, at the same time, the study of the parameter estimation of the spectrumalso have been carried on according to these errors. The further investigations was done onthe basis of "Parameter estimation of the spectrum based on sinc" in this paper. Based onthe fact that current spectrum correction methods almost will lose effect in the condition ofextreme signal, a parameter estimation method of complex frequency spectrum is proposed.The sources of discrete spectrum error is exposed, which is the unique quality of thisalgorithm. From the view of the composing of DFT/FFT leakage spectrum, building theleakage spectrum model to solved all the parameters of the observed signal. Then thepurpose that estimating parameters is realized. The concrete method is establishing acoherent model of the spectrum, decorrelating it through mathematical method to eliminateof spectral leakage error, aliasing error and spectral line interference error of discretespectrum completely from the view of the analytic relationship of each component in DFTspectrum. Previous work has been done that the amplitude expression and the incompletephase expression of the discrete spectrum are obtained through a summarized empiricalformula. The "Parameter estimation of the spectrum based on sinc" is improved, the phaseexpression is given through strict theoretical derivation. At last, VB is used to write thecomputation and simulation software based on the model in this paper. The parameters of complex frequency signal under extreme conditions are estimated, conclusions areobtained that，the parameter estimation algorithm of discrete spectrum proposed in thispaper can eliminate the spectrum error thoroughly, and it is widely applicable and veryimportant in theory. In the condition of low frequency signal, the contrast experiment hasalso been carried out between the Agilent dynamic signal analyzer and the spectrumparameter estimation method based on sinc function, the experiment results prove that theaccuracy of the method presented in this paper is better than the dynamic signal analyzer.But solving this model is very complex, several complex equations are needed to solve.With the increase of the component number in signal, the calculation increases sharply. Sothe algorithm is still not available in engineering, it is expected that the final goal thatapplying it in engineering could be reached by optimizing the algorithm and upgrading thehardware.