Sinusoidal coding is an often employed technique in low bit-rate audio coding. Therefore, methods for efficient quantization of sinusoidal parameters are of great importance. In this paper, we use high-resolution assumptions to derive analytical expressions for the optimal entropy-constrained unrestricted spherical quantizers for the amplitude, phase, and frequency parameters of the sinusoidal model. This is done both for the case of a single sinusoid, and for the more practically relevant case of multiple sinusoids distributed across multiple segments. To account for psychoacoustical effects of the auditory system, a perceptual distortion measure is used. The optimal quantizers minimize a high-resolution approximation of the expected perceptual 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 an objective comparison it is shown that for the squared error distortion measure, the rate-distortion performance of the proposed method is very close to that of the theoretically optimal entropy-constrained vector quantization. Furthermore, for the perceptual distortion measure, the proposed scheme is shown to objectively outperform an existing sinusoidal quantization scheme, where frequency quantization is done independently. Finally, a subjective listening test, in which the proposed scheme is compared to an existing state-of-the-art sinusoidal quantization scheme with fixed quantizers for all input signals, indicates that the proposed scheme leads to an average bit rate reduction of 20%, at the same subjective quality level as the existing scheme

Sinusoidal coding is an essential tool in low-rate audio coding, and developing an efficient quantization scheme for the sinusoidal parameters is therefore crucial. In this work we derive optimal entropy constrained amplitude, phase and frequency quantizers for sinusoids whose frequencies are harmonically related, with respect to the l2distortion measure. This scheme exploits the harmonic structure of many speech and audio signals in the sense that besides amplitudes and phases, only fundamental frequencies need to be quantized, resulting in a significant decrease in the number of bits assigned to frequency parameters. The asymptotically optimal quantizers minimize a high-resolution approximation of the expected l2distortion 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 an objective rate-distortion comparison, the proposed scheme is shown to outperform two variants of a recently proposed scheme, in which all frequency parameters are quantized separately, either directly or differentially

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.