Coding of spectral magnitudes using optimized linear transformations

This paper introduces a novel vector quantization (VQ) technique, wherein the quantized vector is obtained by applying a linear transformation selected from a first codebook to a codevector selected from a second codebook. The transformation is selected from a family of linear transformations, represented by a matrix codebook. Vectors in the second codebook are called residual codevectors. In order to avoid high complexity during the search for the best linear transformation, each linear transformation is assigned a representative vector, such that the search can be done employing the representative vectors. The design algorithm is based on joint optimization of the linear transformation and the residual codebooks. It is shown that the proposed technique yields a high quality spectral magnitude quantizer with performance exceeding that of multistage vector quantizer (MSVQ) of similar complexity and bit rate.