Entropy-constrained polar quantization: theory and an application to audio coding

In this work, we develop entropy-constrained unrestricted polar quantizers, where phase quantization depends on the input amplitude. Formulas for amplitude and phase quantization point densities are derived under high-rate assumptions. It is shown that the mean-squared distortion is decreased considerably as compared to strictly polar quantization and approaches that of scalar rectangular quantization asymptotically with increasing rate. The unrestricted polar quantization is generalized to include a weighted error measure, such that it accounts for masking effects of the human auditory system. Both amplitude and phase quantization depend on the perceptual importance of sinusoids. The new method is applied to a sinusoidal audio coder, and is shown to outperform a conventional sinusoidal quantization method where the number of phase quantization bits is the same for all audible sinusoids.