We propose fast algorithms for computing Discrete Sine and Discrete Cosine Transforms (DCT and DST) of types VI and VII. Particular attention is paid to derivation of fast algorithms for computing DST-VII of lengths 4 and 8, which are currently under consideration for inclusion in ISO/IEC/ITU-T High Efficiency Video Coding (HEVC) standard.

In this paper, an efficient algorithm for implementing MDCT/IMDCT of lengths 5 2Transforms for such lengths are of interest for speech and audio coding applications, such as recently issued and/or emerging standards G.729.1, G.EV-VBR, and EVRC-WB. In our design we utilize a mapping of MDCT of size N into N/2-point DCT-IV and DCT-II with isolated premultiplications, which are subsequently moved in the windowing stage. We show that such a modified window is piece-wise symmetric, and can be stored using N/2 words. In our algorithm we also use an efficient factorization of 5-point DCT-II which requires only 4 multiplications by irrational factors. We compare our proposed algorithm with several alternative implementations and show that our design offers practically appreciable reduction in complexity and memory usage.

No abstract

No abstract

Recently MPEG has developed a new audio coding standard -MPEG-4 AAC Enhanced Low Delay (ELD), targeting low bit rate, full-duplex communication applications such as audio and video conferencing. The AAC-ELD combines low delay SBR filterbank with a low delay core coder filterbank to achieve both high coding efficiency and low algorithmic delay. In this paper, we propose an efficient mapping of the AAC-ELD core coder filterbank to the well known MDCT. This provides a fast algorithm for the new filterbank. Since AAC-LD and AAC-LC profiles also use MDCT filterbank, this mapping enables efficient joint implementation of filterbanks for all 3 profiles. We also present a very efficient 15-point DCT-II algorithm that is useful for implementation of all 3 profiles with frame lengths of 960 and 480. This algorithm requires just 17 multiplications and 67 additions. The overall design structure and complexity analysis of proposed implementation of the filterbanks is also provided.