sine transform

The Fourier sine transform is the imaginary part of the full complex Fourier transform, ℱ_x^(s)[f(x)](k) | = | ℑ[ℱ_x[f(x)](k)] | = | integral_(-∞)^∞ sin(2π k x) f(x) d x. The Fourier sine transform F_s(k) of a function f(x) is implemented as FourierSinTransform[f, x, k], and different choices of a and b can be used by passing the optional FourierParameters -> {a, b} option. In this work, a = 0 and b = - 2π. The discrete Fourier sine transform of a list l of real numbers can be computed in the Wolfram Language using FourierDST[l].

Fourier cosine transform | Fourier transform

Jean-Baptiste-Joseph Fourier