Methodology for approximating and implementing fixed-point approximations of cosines for order-16 DCT

Arianne T. Hinds

doi:10.1117/12.897557

12 September 2011 Methodology for approximating and implementing fixed-point approximations of cosines for order-16 DCT

Arianne T. Hinds

Proceedings Volume 8135, Applications of Digital Image Processing XXXIV; 813504 (2011) https://doi.org/10.1117/12.897557
Event: SPIE Optical Engineering + Applications, 2011, San Diego, California, United States

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.

Citation Download Citation

Arianne T. Hinds "Methodology for approximating and implementing fixed-point approximations of cosines for order-16 DCT", Proc. SPIE 8135, Applications of Digital Image Processing XXXIV, 813504 (12 September 2011); https://doi.org/10.1117/12.897557

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Space operations

Image compression

Video coding

Inspection

Matrix multiplication

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