Error-free computation of 8-point discrete cosine transform based on the Loeffler factorisation and algebraic integers

摘要

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.