High rate spherical quantization of sinusoidal parameters

Quantization of sinusoidal model parameters is of importance in e.g. low-rate audio coding. In this work we introduce entropy constrained unrestricted spherical quantization, where amplitude, phase and frequency are quantized dependently. We derive a high-rate approximation of the average ℓ₂-distortion and use this to analytically derive formulas for optimal spherical scalar quantizers. These quantizers minimize the average distortion, while the corresponding quantization indices satisfy an entropy constraint. The quantizers turn out to be flexible and of low complexity, in the sense that they can be determined for varying entropy constraints without any iterative retraining procedures. As a consequence of minimizing the ℓ₂-norm of the (quantization) error signal, the quantizers depend on both the shape and length of the analysis/synthesis window.