Calculation of an entropy-constrained quantizer for exponentially damped sinudoids parameters

The Exponentially Damped Sinusoids (EDS) model can efficiently represent real-world audio signals. In the context of low bit rate parametric audio coding, the EDS model could bring a significant improvement over classical sinusoidal models. The inclusion of an additional damping parameter calls for a specific quantization scheme. In this report, we describe a new jointscalar quantization scheme for EDS parameters in high resolution hypothesis, which is much easier to implement than a vector quantization scheme. A performance evaluation of this quantizer in comparison with a 3-dimensional vector quantizer is proposed in a paper submitted to IEEE Signal Processing Letters named ”Entropy-Constrained Quantization of Exponentially Damped Sinusoids Parameters”. Index Terms Parametric audio coding, Exponentially Damped Sinusoids, High resolution, Quantization, Entropy A. INTRODUCTION For low bit rate music coding applications, parametric coders are an efficient alternative to transform coders. As a consequence, the interest in parametric audio coding has grown during the last years. Sinusoidal modeling is very popular because most real-world audio signals are dominated by tonal components. In most sinusoidal analysis/synthesis schemes used for parametric coding, sinusoids have constant amplitude over each analysis/synthesis time segment. Sinusoid parameters (amplitude, frequency and phase) are quantized and binary coded. However, some studies have proved that an exponentially damped sinusoidal model (EDS) combined with a variable-length time segmentation is more efficient than a constant-amplitude model. In this report, we describe a joint-scalar quantization method for amplitude, damping and phase parameters. Optimizing the quantizer consists of minimizing the mean distortion under a bit rate constraint. As modern communication techniques commonly use variable-length binary codes, we choose to formulate the bit rate constraint in terms of entropy of quantization indexes. In high resolution hypothesis, i.e. assuming a large number of quantization cells, quantizers are usually defined by their quantization cell density (QCD). The calculation of the optimal QCD is divided in tree parts: first, we calculate the distortion between two exponentially damped sinusoids. Then, assuming dependencies between the quantization of amplitudes, damping and phases, we calculate the mean distortion generated by the quantization process. Finally, we obtain the QCD that minimizes the mean distortion under the entropy constraint. B. THE EDS MODEL AND THE MEAN SQUARE ERROR DISTORTION MEASURE The EDS modeling of a signal x(t), t ∈ [0, T ] can be written as