Abstract
In order to evaluate the accuracy of bispectral estimation method, signals of cosine function were adopted. Because the cosine signals’ three order moment spectrum and three order cumulant spectrum are zero, Non zero part of the bispectrum estimated by no matter which method is the estimation error. Through the comparison of three kinds of estimation methods: the direct method, indirect method and AR parameter method, errors of various estimation methods were obtained, then changing the values of different parameters in all methods, and observing the bispectral error values changes with the parameters, so as to provide a basis for the various bispectrum estimation method and the selection.
Highlights
High Order CumulantIf {x(n)} is the zero mean k order stationary random process, the k order cumulant ckx (τ1,τ 2 , ,τ k−1 ) of the process is defined as the k order joint cumulant of random variable {x (n), x (n +τ1 ), , x (n +τ k−1 )} , namely
In order to evaluate the accuracy of bispectral estimation method, signals of cosine function were adopted
Because the cosine signals’ three order moment spectrum and three order cumulant spectrum are zero, Non zero part of the bispectrum estimated by no matter which method is the estimation error
Summary
If {x(n)} is the zero mean k order stationary random process, the k order cumulant ckx (τ1,τ 2 , ,τ k−1 ) of the process is defined as the k order joint cumulant of random variable {x (n), x (n +τ1 ), , x (n +τ k−1 )} , namely. The k order moment mkx (τ1,τ 2 , ,τ k−1 ) of the process is defined as the k order joint moment of the random variable {x (n), x (n +τ1 ), , x (n +τ k−1 )} , namely. The k-order cumulant spectrum is defined as k − 1 dimension Fourier transform of k order cumulant. K order moment spectrum is defined as k − 1 dimension Fourier transform of k order moment. The most commonly used high order spectrum is the third-order spectrum ( known as the double spectrum), and the estimation formula as follows:. The high order moment spectrum is generally estimated, order. The Formula (7) can be used to calculate the double spectrum by the following formula:
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