Optimization of weighting factors for multiple window time-frequency analysis

This paper concerns the optimal weighting factors for multiple window spectrogram estimation of different stationary and non-stationary processes. The choice of windows are of course important but the weighting factors in the average of the different spectrograms are as important. The criterion for optimization is the normalized mean square error where the normalization factor is the spectrogram estimate. 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 estimation. The optimization is compared for a number of well known sets of multiple windows and the results show that the number as well as the shape of the windows are important factors for a small mean square error.