Editing Discrete sine transform (section)

==Computation==
Although the direct application of these formulas would require O(''N''<sup>2</sup>) operations, it is possible to compute the same thing with only O(''N'' log ''N'') complexity by factorizing the computation similar to the [[fast Fourier transform]] (FFT). (One can also compute DSTs via FFTs combined with O(''N'') pre- and post-processing steps.)

A DST-III or DST-IV can be computed from a DCT-III or DCT-IV (see [[discrete cosine transform]]), respectively, by reversing the order of the inputs and flipping the sign of every other output, and vice versa for DST-II from DCT-II. In this way it follows that types II–IV of the DST require exactly the same number of arithmetic operations (additions and multiplications) as the corresponding DCT types.