As a lapped transform, the MDCT is a bitsomewhat 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]] <math>F\colon \mathbf{R}^{2N} \to \mathbf{R}^N</math> (where '''R''' denotes the set of [[real number]]s). The 2''N'' real numbers ''x''<sub>0</sub>, ..., ''x''<sub>2''N''-1</sub> are transformed into the ''N'' real numbers ''X''<sub>0</sub>, ..., ''X''<sub>''N''-1</sub> according to the formula:
