Finite Fourier Transform

In mathematics the finite Fourier transform may refer to either

  • another name for the discrete Fourier transform

or

  • another name for the Fourier series coefficients

or

  • a transform based on a Fourier-transform-like integral applied to a function, but with integration only on a finite interval, usually taken to be the interval . Equivalently, it is the Fourier transform of a function multiplied by a rectangular window function. That is, the finite Fourier transform of a function on the finite interval is given by:

Famous quotes containing the words finite and/or transform:

    “The finite is annihilated in the presence of the infinite, and becomes a pure nothing. So our spirit before God, so our justice before divine justice.”
    —Blaise Pascal (1623–1662)

    “He had said that everything possessed
    The power to transform itself, or else,
    And what meant more, to be transformed.”
    —Wallace Stevens (1879–1955)