A Note on the MDCT/MDST and Pseudoinverse Matrix

Abstract

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 (TDAC) employed in the current international audio coding standards and commercial audio compression products. Based on the matrix representation of MDCTs and MDSTs 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.