Fast Algorithms For MDCT And Low Delay Filterbanks Used In Audio Coding
Abstract
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.