Pointwise comparison of PCM and \(\Sigma \Delta \) quantization
A quantitative comparison of Pulse Code Modulation (PCM) and Sigma-Delta (\(\Sigma\Delta\)) quantisation methods is made in the setting of finite frames. PCM and \(\Sigma\Delta\) are two industry-standard quantization methods, and the setting of finite frames is appropriate for a host of modern applications. Previous results for this comparison are known for upper error bounds, where \(\Sigma\Delta\) performs better in the setting of frames while PCM is optimal for orthonormal bases. The paper considers the question, whether there are signals such that the corresponding PCM error is smaller than the \(\Sigma\Delta\) error in the frame setting. It is proved that, typically, \(\Sigma\Delta\) outperforms PCM, but not always.
scientific article; zbMATH DE number 5797135
scientific article