- 著者
- Kimiko MOTONAKA Tomoya KOSEKI Yoshinobu KAJIKAWA Seiji MIYOSHI
- 出版者
- The Institute of Electronics, Information and Communication Engineers
- 雑誌
- IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences (ISSN:09168508)
- 巻号頁・発行日
- pp.2021EAP1013, (Released:2021-06-01)
- 被引用文献数
- 2
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.
- 著者
- Seiji MIYOSHI Yoshinobu KAJIKAWA
- 出版者
- The Institute of Electronics, Information and Communication Engineers
- 雑誌
- IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences (ISSN:09168508)
- 巻号頁・発行日
- vol.E101-A, no.12, pp.2419-2433, 2018-12-01
- 被引用文献数
- 5
We analyze the behaviors of the FXLMS algorithm using a statistical-mechanical method. The cross-correlation between a primary path and an adaptive filter and the autocorrelation 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 condition that the tapped-delay line is sufficiently long. The obtained equations are deterministic and closed-form. We analytically solve the equations to obtain the correlations and finally compute the mean-square error. The obtained theory can quantitatively predict the behaviors of computer simulations including the cases of both not only white but also nonwhite reference signals. The theory also gives the upper limit of the step size in the FXLMS algorithm.