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In typical signal-compression applications, the transform properties are further improved by using a [[window function]] ''w''<sub>''n''</sub> (''n'' = 0, ..., 2''N''−1) that is multiplied with ''x''<sub>''n''</sub> and ''y''<sub>''n''</sub> in the MDCT and IMDCT formulas, above, in order to avoid discontinuities at the ''n'' = 0 and 2''N'' boundaries by making the function go smoothly to zero at those points. (That is, we window the data ''before'' the MDCT and ''after'' the IMDCT.) In principle, ''x'' and ''y'' could have different window functions, and the window function could also change from one block to the next (especially for the case where data blocks of different sizes are combined), but for simplicity we consider the common case of identical window functions for equal-sized blocks.
The transform remains invertible (that is, TDAC works), for a symmetric window ''w''<sub>''n''</sub> = ''w''<sub>2''N''−1−''n''</sub>, as long as ''w'' satisfies the
:<math>w_n^2 + w_{n + N}^2 = 1</math>.
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