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Inverse Discrete Fourier Transform

The inverse discrete Fourier transform recovers a finite sequence f_0,...,f_(N-1) from its discrete Fourier transform F_0,...,F_(N-1) by

f_k=1/Nsum_(n=0)^(N-1)F_ne^(2piikn/N),

for k=0, 1, ..., N-1. The normalization and the signs in the exponents depend on convention, but the forward and inverse transforms must use reciprocal choices.

See also

Discrete Fourier Transform, Fast Fourier Transform, Inverse Fourier Transform

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References

Brigham, E. O. The Fast Fourier Transform and Its Applications. Englewood Cliffs, NJ: Prentice-Hall, 1988.

Cite this as:

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

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