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**An efficient computing of oddly stacked MDCT/MDST via evenly stacked MDCT/MDST and vice versa.**
*(English)*
Zbl 1148.94328

Summary: New fast algorithms for the evenly stacked and oddly stacked modified discrete cosine transform (MDCT) and modified discrete sine transform (MDST) computation are proposed. Although the evenly and oddly stacked MDCT/MDST are quite different filter banks based on time domain aliasing cancellation (TDAC), there exists an intimate relation between them, and consequently, the efficient computing of oddly stacked MDCT/MDST can be realized via the evenly stacked MDCT/MDST and vice versa only by simple pre- and post-processing of input and output data sequences. This fact allows to handle the evenly and oddly stacked MDCT/MDST in a unified framework. In particular, it is shown that the transposed evenly and oddly stacked MDCT and MDST matrices are actually the pseudoinverses of their corresponding forward transform matrices. The regular generalized signal flow graphs define interrelated sparse matrix factorizations of the evenly and oddly stacked MDCT/MDST matrices. The proposed new fast algorithms provide efficient implementations of the oddly stacked MDCT in layer III of MPEG (MP3) audio coding. Complete signal flow graphs for the efficient implementation of the MDCT in MP3 and comparison with existing efficient modified/corrected implementations are also presented.

### MSC:

94A11 | Application of orthogonal and other special functions |