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A note on the MDCT/MDST and pseudoinverse matrix. (English) Zbl 1092.65124
Summary: The modified discrete cosine transform (MDCT) and modified discrete sine transform (MDST) both for the evenly and oddly stacked systems are perfect reconstruction cosine/ sine-modulated filter banks based on time domain aliasing cancellation employed in the current international audio coding standards and commercial audio compression products. Based on the matrix representation of MDCT’s and MDST’s it is shown that the transposed MDCT and MDST matrices are actually the pseudoinverses of their corresponding forward transform matrices. The pseudoinverse matrix and its properties provide an elegant mathematical tool to characterize the MDCT/MDST as the analysis/synthesis filter banks in the matrix representation.

MSC:
65T50 Numerical methods for discrete and fast Fourier transforms
15A09 Theory of matrix inversion and generalized inverses
Software:
MDCT/MDST
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