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The MDCT can be calculated using FFT. The naive approach, though, requires
a length FFT for a length block, because of the odd
transform. There are faster approaches though [6]. The MDCT can
be rewritten as an oddtime oddfrequency discrete Fourier transform
(ODFT)

(23) 
[6] presents a fast algorithm for calculating

(24) 
as
where

(28) 
Thus, the MDCT can be calculated using only one point FFT and some
pre and postrotation of the sample points. The IMDCT can be calculated in
a similar way. See the code for a more detailed description.
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