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This chapter shows that the MDCT analysis polyphase matrix can be factorized into three simple building blocks: a sparse “folding” matrix, a diagonal delay matrix, and a DCT-IV transform. This reveals why MDCT/IMDCT implementations are efficient and how perfect reconstruction (PR) follows from simple algebraic properties of the factors.

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Sparse Matrices and the MDCT

  • 章节

  • 发表日期：

    2026年

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  • Gerald Schuller

摘要

This chapter shows that the MDCT analysis polyphase matrix can be factorized into three simple building blocks: a sparse “folding” matrix, a diagonal delay matrix, and a DCT-IV transform. This reveals why MDCT/IMDCT implementations are efficient and how perfect reconstruction (PR) follows from simple algebraic properties of the factors.