The Fourier sine transform is the imaginary part of the full complex Fourier transform,

The Fourier sine transform of a function is implemented as FourierSinTransform[f, x, k], and different choices of and can be used by passing the optional FourierParameters -> a, b option. In this work, and .

The discrete Fourier sine transform of a list of real numbers can be computed in Mathematica using FourierSCT[l].

Press, W. H.; Flannery, B. P.; Teukolsky, S. A.; and Vetterling, W. T. "FFT of Real Functions, Sine and Cosine Transforms." §12.3 in Numerical Recipes in FORTRAN: The Art of Scientific Computing, 2nd ed. Cambridge, England: Cambridge University Press, pp. 504-515, 1992.

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Weisstein, Eric W. "Fourier Sine Transform." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/FourierSineTransform.html