The Volterra filter is one of the digital filters that can describe nonlinearity. In this paper, we analyze the dynamic behaviors of an adaptive signal-processing system including the Volterra filter by a statistical-...
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The Volterra filter is one of the digital filters that can describe nonlinearity. In this paper, we analyze the dynamic behaviors of an adaptive signal-processing system including the Volterra filter by a statistical-mechanical method. On the basis of the self-averaging property that holds when the tapped delay line is assumed to be infinitely long, we derive simultaneous differential equations in a deterministic and closed form, which describe the behaviors of macroscopic variables. We obtain the exact solution by solving the equations analytically. In addition, the validity of the theory derived is confirmed by comparison with numerical simulations.
We analyze the learning curves of the FXLMS algorithm using a statistical-mechanical method when the reference signal is not necessarily white. We treat the nonwhite reference signal by introducing the correlation fun...
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ISBN:
(纸本)9781479903566
We analyze the learning curves of the FXLMS algorithm using a statistical-mechanical method when the reference signal is not necessarily white. We treat the nonwhite reference signal by introducing the correlation function of the signal to the method proposed in our previous study. Cross-correlations between the element of a primary path and that of an adaptive filter and autocorrelations of the elements of the adaptive filter are treated as macroscopic variables. We obtain simultaneous differential equations that describe the dynamical behaviors of the macroscopic variables under the conditions in which the tapped-delay line is long. We analytically solve the equations to obtain the correlations and finally compute the mean-square error. The obtained theory quantitatively agrees with the results of computer simulations. The theory also gives the upper limit of the step size in the FXLMS algorithm.
We analyze the learning curves of the FXLMS algorithm using a statistical-mechanical method when the reference signal is not necessarily white. We treat the nonwhite reference signal by introducing the correlation fun...
详细信息
ISBN:
(纸本)9781479903573
We analyze the learning curves of the FXLMS algorithm using a statistical-mechanical method when the reference signal is not necessarily white. We treat the nonwhite reference signal by introducing the correlation function of the signal to the method proposed in our previous study. Cross-correlations between the element of a primary path and that of an adaptive filter and autocorrelations of the elements of the adaptive filter are treated as macroscopic variables. We obtain simultaneous differential equations that describe the dynamical behaviors of the macroscopic variables under the conditions in which the tapped-delay line is long. We analytically solve the equations to obtain the correlations and finally compute the mean-square error. The obtained theory quantitatively agrees with the results of computer simulations. The theory also gives the upper limit of the step size in the FXLMS algorithm.
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