Fast Algorithms For MDCT And Low Delay Filterbanks Used In Audio Coding
Modern audio and speech coding systems use filterbank and transform coding techniques to decorrelate the input signal. Cosine-modulated, perfect reconstruction, pseudo-QMF filterbanks are most commonly used for this purpose. In this thesis, we present three propositions. First, a fast algorithm for modified discrete cosine transform (MDCT) for transform lengths of the form 5× 2m and 15× 2m is presented. This algorithm is based on mapping the MDCT to DCT-II via DCT-IV and using the involutory property of the DCT-IV matrix. This leads to a reduction in the number of multiplications and constant memory requirement. The algorithm also uses very efficient DCT-II modules for transform lengths of 5 and 15 which are derived from the Winograd Fourier Transform Algorithm. Second, the newly introduced MPEG-4 AAC Enhanced Low Delay filterbanks are mapped to MDCT. The mapping involves just input and output permutations, sign changes and additions. Since many fast algorithms exist for MDCT, this mapping essentially provides a fast algorithm for the new filterbanks. Third, we present a radix-5 decomposition for DCT-II useful for MDCT of length 5× 2m. This decomposition is useful for improving the precision of the fixedpoint implementations of the algorithms. Complexity analysis is provided for all the algorithms and comparisons are made with existing algorithms.