By Topic

Worst-case error analysis of lifting-based fast DCT-algorithms

Sign In

Cookies must be enabled to login.After enabling cookies , please use refresh or reload or ctrl+f5 on the browser for the login options.

Formats Non-Member Member
$31 $13
Learn how you can qualify for the best price for this item!
Become an IEEE Member or Subscribe to
IEEE Xplore for exclusive pricing!
close button

puzzle piece

IEEE membership options for an individual and IEEE Xplore subscriptions for an organization offer the most affordable access to essential journal articles, conference papers, standards, eBooks, and eLearning courses.

Learn more about:

IEEE membership

IEEE Xplore subscriptions

1 Author(s)
Primbs, M. ; Inst. fur Math., Univ. Duisburg-Essen, Duisburg, Germany

Integer DCTs have a wide range of applications in lossless coding, especially in image compression. An integer-to-integer DCT of radix-2-length n is a nonlinear, left-invertible mapping, which acts on Zn and approximates the classical discrete cosine transform (DCT) of length n. All known integer-to-integer DCT-algorithms of length 8 are based on factorizations of the cosine matrix C8II into a product of sparse matrices and work with lifting steps and rounding off. For fast implementation one replaces floating point numbers by appropriate dyadic rationals. Both rounding and approximation leads to truncation errors. In this paper, we consider an integer-to-integer transform for (2×2) rotation matrices and give estimates of the truncation errors for arbitrary approximating dyadic rationals. Further, using two known integer-to-integer DCT-algorithms, we show examplarily how to estimate the worst-case truncation error of lifting based integer-to-integer algorithms in fixed-point arithmetic, whose factorizations are based on (2×2) rotation matrices.

Published in:

Signal Processing, IEEE Transactions on  (Volume:53 ,  Issue: 8 )