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Fourier Cosine Transform

The Fourier cosine transform of a real function is the real part of the full complex Fourier transform,

F_x^((c))[f(x)](k)=R[F_x[f(x)](k)]
(1)
=int_(-infty)^inftycos(2pikx)f(x)dx.
(2)

The Fourier cosine transform F_c(k) of a function f(x) is implemented as FourierCosTransform[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=-2pi.

The discrete Fourier cosine transform of a list l of real numbers can be computed in the Wolfram Language using FourierDCT[l].

See also

Fourier Sine Transform, Fourier Transform

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References

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.

Referenced on Wolfram|Alpha

Fourier Cosine Transform

Cite this as:

Weisstein, Eric W. "Fourier Cosine Transform." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/FourierCosineTransform.html

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