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A new method for efficient digitizing analog signals while preserving the original waveform as close as possible with respect to the relative quantization error is presented. Logarithmic quantization is applied to short vectors of samples represented in sphere coordinates. The resulting advantages, i.e. a constant Signal-to-Noise Ratio over a very high dynamic range at a small loss with respect to rate-distortion theory are discussed. In order to increase the Signal-to-Noise Ratio (SNR) by exploitation of correlations within the source signal, a method of combining differential pulse code modulation (DPCM) with spherical logarithmic quantization is presented. The resulting technique achieves an efficient digital representation of waveforms with a high long term as well as segmental SNR at an extreme low delay of the signal.

Spherical logarithmic quantization and its application for DPCM