caa a22 4500 463246837 CHVBK 20180405153328.0 cr unu---uuuuu 170326e20070601xx s 000 0 eng 10.1007/s00041-006-6032-y doi (NATIONALLICENCE)springer-10.1007/s00041-006-6032-y Smooth Frame-Path Termination for Higher Order Sigma-Delta Quantization [Elektronische Daten] [Bernhard G. Bodmann, Vern I. Paulsen, Soha A. Abdulbaki] We study the performance of finite frames for the encoding of vectors by applying standard higher-order sigma-delta quantization to the frame coefficients. Our results are valid for any quantizer with accuracy ε > 0 operating in the no-overload regime. The frames under consideration are obtained from regular sampling of a path in a Hilbert space. In order to achieve error bounds that are comparable to results on higher-order sigma-delta for the quantization of oversampled bandlimited functions, we construct frame paths that terminate smoothly in the zero vector, that is, with an appropriate number of vanishing derivatives at the endpoint. Birkhauser Boston, 2007 Bodmann Bernhard G. Department of Applied Mathematics, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada aut Paulsen Vern I. Department of Mathematics, University of Houston, 4800 Calhoun Road, Houston, TX 77204-3008, USA aut Abdulbaki Soha A. Department of Mathematics, University of Houston, 4800 Calhoun Road, Houston, TX 77204-3008, USA aut Journal of Fourier Analysis and Applications Birkhäuser-Verlag; www.birkhauser.com 13/3(2007-06-01), 285-307 1069-5869 13:3<285 2007 13 41 https://doi.org/10.1007/s00041-006-6032-y text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00041-006-6032-y text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Bodmann Bernhard G. Department of Applied Mathematics, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada aut NATIONALLICENCE 700 1- Paulsen Vern I. Department of Mathematics, University of Houston, 4800 Calhoun Road, Houston, TX 77204-3008, USA aut NATIONALLICENCE 700 1- Abdulbaki Soha A. Department of Mathematics, University of Houston, 4800 Calhoun Road, Houston, TX 77204-3008, USA aut NATIONALLICENCE 773 0- Journal of Fourier Analysis and Applications Birkhäuser-Verlag; www.birkhauser.com 13/3(2007-06-01), 285-307 1069-5869 13:3<285 2007 13 41 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer