DFTJEW: Difference between revisions
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The [[FourierTransformsJW|Fourier Transform]] is a powerful tool to convert a continuous function from the time domain into the frequency domain. The Fourier transform, however, is an integral transform; it is done by integration. This cannot be done with a discrete function. The Discrete Fourier Transform (DFT) allows us to transform a discrete function from the time domain into the frequency domain. |
The [[FourierTransformsJW|Fourier Transform]] is a powerful tool to convert a continuous function from the time domain into the frequency domain. The Fourier transform, however, is an integral transform; it is done by integration. This cannot be done with a discrete function. The Discrete Fourier Transform (DFT) allows us to transform a discrete function from the time domain into the frequency domain. |
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If <math>x(n)</math> is a discrete function in time, then the DFT of <math>x(n)</math> would be: |
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Then the DFT of <math>x(n)</math> would be: |
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<math>\mbox{DFT}[x(n)] \equiv X(m) \equiv \sum_{n=0}^{N-1} x(n) e^{-j \frac{2 \pi n m}{N} }</math> |
<math>\mbox{DFT}[x(n)] \equiv X(m) \equiv \sum_{n=0}^{N-1} x(n) e^{-j \frac{2 \pi n m}{N} }</math> |
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Revision as of 15:13, 6 December 2005
Discrete Fourier Transform
The Fourier Transform is a powerful tool to convert a continuous function from the time domain into the frequency domain. The Fourier transform, however, is an integral transform; it is done by integration. This cannot be done with a discrete function. The Discrete Fourier Transform (DFT) allows us to transform a discrete function from the time domain into the frequency domain.
If is a discrete function in time, then the DFT of would be:
![{\displaystyle {\mbox{DFT}}[x(n)]\equiv X(m)\equiv \sum _{n=0}^{N-1}x(n)e^{-j{\frac {2\pi nm}{N}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/97b475699f963ff622b0f1a84f1ee25c9a127abb)
Principle author: Jeffrey Wonoprabowo