Pointwise comparison of PCM and \(\Sigma \Delta \) quantization
type: Item
instance of: scholarly article
title: Pointwise comparison of PCM and \(\Sigma \Delta \) quantization
zbMATH Open document ID: 1210.94064
author: John J. Benedetto
author: Onur Oktay
published in: Constructive Approximation
publication date: 2010-10-07T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 94A14
Mathematics Subject Classification ID: 41A29
Mathematics Subject Classification ID: 42C40
Mathematics Subject Classification ID: 94A12
Mathematics Subject Classification ID: 94A20
zbMATH DE Number: 5797135
zbMATH Keywords: frames
zbMATH Keywords: Sigma-Delta quantization
zbMATH Keywords: pulse code modulation
reviewed by: Gerlind Plonka
MaRDI profile type: Publication
full work available at URL: s00365-010-9083-x
OpenAlex ID: W2134693873
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DOI: 10.1007/S00365-010-9083-X
description: scientific article; zbMATH DE number 5797135