Tuyển tập các báo cáo nghiên cứu về sinh học được đăng trên tạp chí sinh học Journal of Biology đề tài: Research Article Optimization of Weighting Factors for Multiple Window Spectrogram of Event-Related Potentials Maria Hansson-Sandsten (EURASIP Member) and Johan Sandberg (EURASIP Member) | Hindawi Publishing Corporation EURASIP Journal on Advances in Signal Processing Volume 2010 Article ID 391798 10 pages doi 2010 391798 Research Article Optimization of Weighting Factors for Multiple Window Spectrogram of Event-Related Potentials Maria Hansson-Sandsten EURASIP Member and Johan Sandberg EURASIP Member Division of Mathematical Statistics Centre for Mathematical Sciences Lund University Box 118 221 00 Lund Sweden Correspondence should be addressed to Maria Hansson-Sandsten sandsten@ Received 22 December 2009 Accepted 14 May 2010 Academic Editor Lutfiye Durak Copyright 2010 M. Hansson-Sandsten and J. Sandberg. 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. This paper concerns the mean square error optimal weighting factors for multiple window spectrogram of different stationary and nonstationary processes. It is well known that the choice of multiple windows is important but here we show that the weighting of the different multiple window spectrograms in the final average is as important to consider and that the equally averaged spectrogram is not mean square error optimal for non-stationary processes. The cost function for optimization is the normalized mean square error where the normalization factor is the multiple window spectrogram. This means that the unknown weighting factors will be present in the numerator as well as in the denominator. A quasi-Newton algorithm is used for the optimization. The optimization is compared for a number of well-known sets of multiple windows and common weighting factors and the results show that the number and the shape of the windows are important for a small mean square error. Multiple window spectrograms using these optimal weighting factors from ElectroEncephaloGram data including steady-state visual evoked potentials are shown as
