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or equivalently an N × N square matrix. There are several variants of the DST with slightly modified definitions. The N real numbers x₀, ..., x_N-1 are transformed into the N real numbers X₀, ..., X_N-1 according to one of the formulas:

DST-I

:

The DST-I matrix is orthogonal (up to a scale factor).

A DST-I is exactly equivalent to a DFT of a real sequence that is odd around the zeroth

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