DFTJEW: Difference between revisions
| Line 5: | Line 5: | ||
<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> |
||
When dealing with a continuous function, an inverse Fourier Transform can be used to go back from the frequency domain into the time domain. The discete analog of the inverse Fourier Transform is the IDFT (Inverse Discrete Fourier Transform) which is defined below: |
|||
<math> \mbox{IDFT}[X(m)] \equiv x(k) \equiv \frac{1}{N} \sum_{m=0}^{N-1} X(m) e^{j \frac{2 \pi k m}{N} } </math> |
|||
Revision as of 14:30, 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)
When dealing with a continuous function, an inverse Fourier Transform can be used to go back from the frequency domain into the time domain. The discete analog of the inverse Fourier Transform is the IDFT (Inverse Discrete Fourier Transform) which is defined below:
![{\displaystyle {\mbox{IDFT}}[X(m)]\equiv x(k)\equiv {\frac {1}{N}}\sum _{m=0}^{N-1}X(m)e^{j{\frac {2\pi km}{N}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/18a153b7ddc77ab5058148591b6bd1aa3f6d2579)
Principle author: Jeffrey Wonoprabowo