High resolution spherical quantization of sinusoidal parameters using a perceptual distortion measure

Sinusoidal modelling is a key technology in low rate audio coding, and methods for efficient quantization of sinusoidal parameters are therefore of high importance. We derive analytical formulas for the optimal entropy constrained unrestricted spherical quantizers for amplitude, phase and frequency, using a perceptual distortion measure. This is done both for a single sinusoid, and for multiple sinusoids distributed over multiple segments. The quantizers minimize a high-resolution approximation of the expected 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 easily for varying bit rate requirements, without any sort of retraining or iterative procedures. In objective and subjective comparison tests, the proposed method is shown to outperform an existing state-of-the-art sinusoidal quantization scheme, where quantization of frequency parameters is done independently.