Fourier transform - Definition. Was ist Fourier transform
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Was (wer) ist Fourier transform - definition


Fourier transform         
  • chord]]. The first three peaks on the left correspond to the frequencies of the [[fundamental frequency]] of the chord (C, E, G). The remaining smaller peaks are higher-frequency [[overtone]]s of the fundamental pitches. A [[pitch detection algorithm]] could use the relative intensity of these peaks to infer which notes the pianist pressed.
  • Some problems, such as certain differential equations, become easier to solve when the Fourier transform is applied. In that case the solution to the original problem is recovered using the inverse Fourier transform.
  • Animation showing the Fourier Transform of a time shifted signal. [Top] the original signal (yellow), is continuously time shifted (blue). [Bottom] The resultant Fourier Transform of the time shifted signal. Note how the higher frequency components revolve in complex plane faster than the lower frequency components.
  • The [[rectangular function]] is [[Lebesgue integrable]].
  • The [[sinc function]], which is the Fourier transform of the rectangular function, is bounded and continuous, but not Lebesgue integrable.
MATHEMATICAL TRANSFORM THAT EXPRESSES A FUNCTION OF TIME AS A FUNCTION OF FREQUENCY
Fourier Transform; Fourier integral; Fourier transforms; Fourier transformation; Reality condition; ℱ; Continuous fourier transform; Continuous Fourier transform; CTFT; Forier transform; Fourier Transformation; Fourrier transform; Fourier shift theorem; List of Fourier transforms; Fourier wave analysis; Fourier uncertainty principle; Fourier component; Fourier transformations; Table of Fourier transforms; Fourier components; F-hat; Continuous-time Fourier transform
A Fourier transform (FT) is a mathematical transform that decomposes functions depending on space or time into functions depending on spatial frequency or temporal frequency. That process is also called analysis.
https://en.wikipedia.org/wiki/Fourier_transform
Fourier transform         
  • chord]]. The first three peaks on the left correspond to the frequencies of the [[fundamental frequency]] of the chord (C, E, G). The remaining smaller peaks are higher-frequency [[overtone]]s of the fundamental pitches. A [[pitch detection algorithm]] could use the relative intensity of these peaks to infer which notes the pianist pressed.
  • Some problems, such as certain differential equations, become easier to solve when the Fourier transform is applied. In that case the solution to the original problem is recovered using the inverse Fourier transform.
  • Animation showing the Fourier Transform of a time shifted signal. [Top] the original signal (yellow), is continuously time shifted (blue). [Bottom] The resultant Fourier Transform of the time shifted signal. Note how the higher frequency components revolve in complex plane faster than the lower frequency components.
  • The [[rectangular function]] is [[Lebesgue integrable]].
  • The [[sinc function]], which is the Fourier transform of the rectangular function, is bounded and continuous, but not Lebesgue integrable.
MATHEMATICAL TRANSFORM THAT EXPRESSES A FUNCTION OF TIME AS A FUNCTION OF FREQUENCY
Fourier Transform; Fourier integral; Fourier transforms; Fourier transformation; Reality condition; ℱ; Continuous fourier transform; Continuous Fourier transform; CTFT; Forier transform; Fourier Transformation; Fourrier transform; Fourier shift theorem; List of Fourier transforms; Fourier wave analysis; Fourier uncertainty principle; Fourier component; Fourier transformations; Table of Fourier transforms; Fourier components; F-hat; Continuous-time Fourier transform
¦ noun Mathematics a function derived from a given non-periodic function and representing it as a series of sinusoidal functions.
Fourier transform         
  • chord]]. The first three peaks on the left correspond to the frequencies of the [[fundamental frequency]] of the chord (C, E, G). The remaining smaller peaks are higher-frequency [[overtone]]s of the fundamental pitches. A [[pitch detection algorithm]] could use the relative intensity of these peaks to infer which notes the pianist pressed.
  • Some problems, such as certain differential equations, become easier to solve when the Fourier transform is applied. In that case the solution to the original problem is recovered using the inverse Fourier transform.
  • Animation showing the Fourier Transform of a time shifted signal. [Top] the original signal (yellow), is continuously time shifted (blue). [Bottom] The resultant Fourier Transform of the time shifted signal. Note how the higher frequency components revolve in complex plane faster than the lower frequency components.
  • The [[rectangular function]] is [[Lebesgue integrable]].
  • The [[sinc function]], which is the Fourier transform of the rectangular function, is bounded and continuous, but not Lebesgue integrable.
MATHEMATICAL TRANSFORM THAT EXPRESSES A FUNCTION OF TIME AS A FUNCTION OF FREQUENCY
Fourier Transform; Fourier integral; Fourier transforms; Fourier transformation; Reality condition; ℱ; Continuous fourier transform; Continuous Fourier transform; CTFT; Forier transform; Fourier Transformation; Fourrier transform; Fourier shift theorem; List of Fourier transforms; Fourier wave analysis; Fourier uncertainty principle; Fourier component; Fourier transformations; Table of Fourier transforms; Fourier components; F-hat; Continuous-time Fourier transform
<mathematics> A technique for expressing a waveform as a weighted sum of sines and cosines. Computers generally rely on the version known as {discrete Fourier transform}. Named after J. B. Joseph Fourier (1768 -- 1830). See also wavelet, discrete cosine transform. (1997-03-9)
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