Dirichlet mixture modeling to estimate an empirical lower bound for LSF quantization

The line spectral frequencies (LSFs) are commonly used for the linear predictive/autoregressive model in speech and audio coding. Recently, probability density function (PDF)-optimized vector quantization (VQ) has been studied intensively for quantization of LSF parameters. In this paper, we study the VQ performance bound of the LSF parameters. The LSF parameters are transformed to the ΔΔ LSF domain and the underlying distribution of the ΔLSFΔLSF parameters is modeled by a Dirichlet mixture model (DMM) with a finite number of mixture components. The quantization distortion, in terms of the mean squared error (MSE), is calculated with high rate theory. For LSF quantization, 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 (an empirical lower bound) for transparent coding of the LSF under DMM modeling is derived.