Optimization of Weighting Factors for Multiple Window Spectrogram of Event-Related Potentials

Abstract

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 examples.