Open AccessError‐free computation of 8‐point discrete cosine transform based on the Loeffler factorisation and algebraic integers
Author(s) -
Coelho Diego F.G.,
Cintra Renato J.,
Kulasekera Sunera,
Madanayake Arjuna,
Dimitrov Vassil S.
Publication year - 2016
Publication title -
iet signal processing
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.384
H-Index - 42
ISSN - 1751-9683
DOI - 10.1049/iet-spr.2015.0175
Subject(s) - discrete cosine transform , algorithm , gate array , algebraic number , computer science , floating point , factorization , very large scale integration , mathematics , field programmable gate array , computer hardware , artificial intelligence , image (mathematics) , embedded system , mathematical analysis
An 8‐point discrete cosine transform (DCT) fast algorithm based on the Loeffler DCT factorisation and algebraic integer (AI) representation is proposed. The proposed algorithm is an error‐free implementation of the Loeffler algorithm and it is capable of computing the 8‐point DCT multiplierlessly. Decoding architectures are also proposed for mapping AI encoded quantities back to usual fixed point arithmetic using canonical signed digit representation and the expansion factor method. The proposed algorithm is mapped into systolic‐array digital architectures and physically realised as digital prototype circuits using field‐programmable gate array technology on a Reconfigurable Open Architecture Computing Hardware board and mapped to 0.18 μm complementary metal–oxide–semiconductor technology using AMS Encounter Digital Implementation libraries at 1.8 V supply.