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On the relationship between MDCT, SDPT and DFT

The modified discrete cosine transform (MDCT) has emerged as a dominant time-frequency decomposition method in high quality audio compression. The MDCT is a special case of the lapped transforms (LTs) with 50% overlap. This paper establishes the relationship between the MDCT and shifted discrete Fourier transform (SDFT). The analysis provides insight into the following issues: (1) the relationship between MDCT, shifted DFT (SDFT) and DFT, (2) characteristics of the MDCT in the time and frequency domain, (3) the concept of time domain aliasing cancellation (TDAC).