Journal of Applied Mathematics
Volume 2013 (2013), Article ID 781856, 8 pages
Research Article

Convergence Analysis of EFOP Estimate Based on Frequency Domain Smoothing

School of Software, Tsinghua University, Tsinghua National Laboratory for Information Science and Technology, Beijing 100084, China

Received 8 March 2013; Revised 21 April 2013; Accepted 24 April 2013

Academic Editor: Graziano Chesi

Copyright © 2013 Yulai Zhang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The classic methods for frequency domain transfer function estimation such as the Empirical Transfer Function Estimate (ETFE) and cross spectral method do not work well when the noise signal is complex. Combines the time domain and frequency domain methods the Empirical Frequency-domain Optimal Parameter (EFOP) Estimate was presented. It could improve the precision of system's transfer function estimation and identification efficiency. The convergence of the EFOP based on frequency domain smoothing is investigated in this paper. The transfer function is weighted by a frequency window and the GPE criterion is extended to the integral form. Convergence rate and consistent properties for the EFOP estimate are given. Finally, some simulation results are included to illustrate the advantage of the EFOP based smoothing method.