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Dirichlet Mixture Model based VQ Performance Prediction for Line Spectral Frequency

In this paper, we continue our previous work on the Dirichlet mixture model (DMM)-based VQ to derive the performance bound of the LSF VQ. The LSF parameters are transformed into the $Δ$LSF domain and the underlying distribution of the $Δ$LSF parameters are modelled by a DMM with finite number of mixture components. The quantization distortion, in terms of the mean squared error (MSE), is calculated with the high rate theory. The mapping relation between the perceptually motivated log spectral distortion (LSD) and the MSE is empirically approximated by a polynomial. With this mapping function, the minimum required bit rate for transparent coding of the LSF is estimated.