Synthesis/coding of audio signals using optimized wavelets

A novel audio synthesis/coding approach based on an optimization of the wavelet transform of the audio signal is presented. In each frame of the audio signal, the authors identify the wavelet which yields an approximation to the audio segment that requires the minimum number of bits. The wavelet approximation is constrained to have no perceptual distortion or a distortion that is less than some fixed maximum level. Two wavelet coefficient representations are considered. In the first representation, the quantization step is fixed and the magnitude of the transform coefficients is optimized. In the second approach the wavelet coefficients are adaptively quantized. The authors show that the second representation leads to simpler optimization problems. They suggest several approximations which reduce the complexity of the optimization problem. Experiments indicate that high quality speech and audio reconstruction is possible in the range of 8-9 kb/s