Jointly optimal time segmentation, component selection and quantization for sinusoidal coding of audio and speech

We propose a rate-distortion optimal algorithm for sinusoidal modeling of audio and speech. The algorithm determines, for a pre-specified target bit-rate, the optimal (variable-length) time segmentation, the optimal distribution of sinusoidal components over the segments and the optimal (scalar) quantizers for quantizing the sinusoid parameters. The optimization is done by jointly optimizing the segment lengths, number of sinusoids and quantizers using high-resolution quantization theory and dynamic programming techniques, which makes it possible to solve the algorithm in polynomial time. A particular advantage of the proposed method is that, given a target bit-rate, it solves the problem of finding the optimal balance between total number of sinusoids and number of bits per sinusoid.