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Formally, the discrete sine transform is a linear, invertible function F: R < sup > N </ sup > < tt >-></ tt > R < sup > N </ sup > ( where R denotes the set of real numbers ), or equivalently an N × N square matrix.
There are several variants of the DST with slightly modified definitions.
The N real numbers x < sub > 0 </ sub >, ...., x < sub > N-1 </ sub > are transformed into the N real numbers X < sub > 0 </ sub >, ..., X < sub > N-1 </ sub > according to one of the formulas:
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