Bernd Matschkal

Spherical Logarithmic Quantization

Band 19, Erlanger Berichte aus Informations- und Kommunikationstechnik, Herausgeber: A. Kaup, W. Koch, J. Huber. Shaker Verlag, Aachen, 2008.


Spherical logarithmic quantization (SLQ) is a vector quantization method for efficiently digitizing analog signals at a high dynamic range and with very low distortion while preserving the original waveform as closely as possible. Hence, the achieved quality can be measured with respect to objective scales like signal-to-noise ratio (SNR) and listening evaluations for an averaged perceived audio quality are not necessary. Moreover SLQ is able to operate at a low data rate of e.g. 2 bits per sample and at a very low signal delay of about 10 samples, this corresponds to approximately 200Ás for high quality audio signals. The technique of SLQ is universally applicable (i.e. not restricted to e.g. audio signals) and achieves an efficient digital representation of waveforms with high longterm as well as high segmental signal-to-noise ratios. The aim of this thesis is to give a detailed description of the SLQ algorithm and to present simulation results on the performance of this new quantization scheme that combines several advantages. After a review of some important basic principles concerning quantization and linear prediction, the SLQ encoder is described. To short vectors of signal samples which are represented in sphere coordinates, logarithmic quantization is applied to the radius and uniform quantization is applied to the angles. This results in the advantage of a constant signal-to-noise ratio over a very high dynamic range at a small loss with respect to the rate-distortion theory. In order to increase the signal-to-noise ratio by exploitation of correlations within the source signal, a solution for the problem of combining this vector quantization scheme with differential pulse code modulation (DPCM) is presented. This approach is also extended towards adaptive prediction. An indexing scheme for the quantization cells covering the surface of a multidimensional unit sphere is presented for both the encoder and the decoder side. Since many audio examples are given within the scope of this thesis, an additional feature to increase the perceptional quality is introduced. Furthermore this thesis includes numerous simulation results on the SNR performance of SLQ for both ideal error-free digital communication and transmission over noisy erroneous channels.