On the relationship between mdct, sdft and dft

摘要

Modified Discrete Cosing Transform (MDCT) has emerged as a dominant time-frequency decomosition method in high quality audio compression. The MDCT is a special case of the Lapped Transforms (LTs) with 50percent 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).