Definition
As a lapped transform, the MDCT is a bit unusual compared to other Fourier-related transforms in that it has half as many outputs as inputs (instead of the same number). In particular, it is a linear function (where R denotes the set of real numbers). The 2N real numbers x0, ..., x2N-1 are transformed into the N real numbers X0, ..., XN-1 according to the formula:
(The normalization coefficient in front of this transform, here unity, is an arbitrary convention and differs between treatments. Only the product of the normalizations of the MDCT and the IMDCT, below, is constrained.)
Read more about this topic: Modified Discrete Cosine Transform
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