Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Quantization Noise Shaping on Arbitrary Frame Expansions | Hindawi Publishing Corporation EURASIP Journal on Applied Signal Processing Volume 2006 Article ID 53807 Pages 1-12 DOI ASP 2006 53807 Quantization Noise Shaping on Arbitrary Frame Expansions Petros T. Boufounos and Alan V. Oppenheim Digital Signal Processing Group Massachusetts Institute of Technology 77 Massachusetts Avenue Room 36-615 Cambridge MA 02139 USA Received 2 October 2004 Revised 10 June 2005 Accepted 12 July 2005 Quantization noise shaping is commonly used in oversampled A D and D A converters with uniform sampling. This paper considers quantization noise shaping for arbitrary finite frame expansions based on generalizing the view of first-order classical oversampled noise shaping as a compensation of the quantization error through projections. Two levels of generalization are developed one a special case of the other and two different cost models are proposed to evaluate the quantizer structures. Within our framework the synthesis frame vectors are assumed given and the computational complexity is in the initial determination of frame vector ordering carried out off-line as part of the quantizer design. We consider the extension of the results to infinite shift-invariant frames and consider in particular filtering and oversampled filter banks. Copyright 2006 P. T. Boufounos and A. V. Oppenheim. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited. 1. INTRODUCTION Quantization methods for frame expansions have received considerable attention in the last few years. Simple scalar quantization applied independently on each frame expansion coefficient followed by linear reconstruction is well known to be suboptimal 1 2 . Several algorithms have been proposed that improve performance although with significant complexity either at the quantizer 3 or in the reconstruction method 3 4 . More .
