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Proceedings Paper

Methodology for approximating and implementing fixed-point approximations of cosines for order-16 DCT
Author(s): Arianne T. Hinds
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Paper Abstract

Spatial transformations whose kernels employ sinusoidal functions for the decorrelation of signals remain as fundamental components of image and video coding systems. Practical implementations are designed in fixed precision for which the most challenging task is to approximate these constants with values that are both efficient in terms of complexity and accurate with respect to their mathematical definitions. Scaled architectures, for example, as used in the implementations of the order-8 Discrete Cosine Transform and its corresponding inverse both specified in ISO/IEC 23002-2 (MPEG C Pt. 2), can be utilized to mitigate the complexity of these approximations. That is, the implementation of the transform can be designed such that it is completed in two stages: 1) the main transform matrix in which the sinusoidal constants are roughly approximated, and 2) a separate scaling stage to further refine the approximations. This paper describes a methodology termed the Common Factor Method, for finding fixed-point approximations of such irrational values suitable for use in scaled architectures. The order-16 Discrete Cosine Transform provides a framework in which to demonstrate the methodology, but the methodology itself can be employed to design fixed-point implementations of other linear transformations.

Paper Details

Date Published: 12 September 2011
PDF: 14 pages
Proc. SPIE 8135, Applications of Digital Image Processing XXXIV, 813504 (12 September 2011); doi: 10.1117/12.897557
Show Author Affiliations
Arianne T. Hinds, Ricoh Production Print Solutions (United States)

Published in SPIE Proceedings Vol. 8135:
Applications of Digital Image Processing XXXIV
Andrew G. Tescher, Editor(s)

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