High dimension finite mixture Gaussian model estimation for short time Fourier decomposition by EM-algorithm

A modification of the central limit theorem indicates that for a stationary or asymptotically stationary random process, its Fourier coefficients are independent complex Gaussian random variables in Reedman, D. and Lane, D., (1980). We apply this idea in the short time Fourier transform, where most process has the asymptotic stationary property in short time sense. The estimated parameters of the complex Gaussian distribution can be used in the feature extraction or the plug-in hypothesis test for recognition. The problem becomes to estimate the parameters of the complex Gaussian. The windowed short time Fourier coefficients are not simple complex Gaussian but contaminated Gaussian, which means we need to estimate the parameters of mixture Gaussian. The EM-algorithm could estimate the parameters directly but the M-step is still complicate. Recasting the contaminated Gaussian as a finite mixture Gaussian model, we can estimated the mean vector and covariance matrix for each time-frequency bin. Estimate the parameters of a mixture high-dimension joint Gaussian distribution with high accuracy and low computation cost shows a good way to solve the problem of distribution estimation. With the estimated distribution, we can create a statistical model for recognition. This method is examined with a mixture 2 dimension joint Gaussian distribution and the simulation results are discussed with good performance. The convergence preserved by the EM-algorithm and the convergence rate is examined too.