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The FFT is an efficient algorithm to compute the discrete Fourier transform (DFT).

The FFT transforms a time signal x to a frequency signal X. And vice versa, the IFFT transforms a frequency signal X to a time signal x.

FFT | IFFT |
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${X}_{k}={\displaystyle \sum _{n=0}^{N-1}{x}_{n}}{e}^{-j2\pi k\frac{n}{N}}$ | ${x}_{k}=\frac{1}{N}{\displaystyle \sum _{n=0}^{N-1}{X}_{n}}{e}^{j2\pi k\frac{n}{N}}$ |

The spectrum analysis (FFT) and signal synthesis (IFFT) equations look quite similar apart from the term $\frac{1}{N}$. This asymmetry leads to a power variation of the time and frequency signal.

See also

Create your individual signal spectra by using the FFT calculator. Click on the start button above!

Enter the time domain samples. Press *Submit* to calculate the frequency domain result.

- The data size must be a power of 2: 2, 4, 8, 16, 32...
- The format is compatible with Excel: the sequence of complex numbers can be copied from and to spreadsheets.

Some examples illustrate the Fast Fourier transform. Time signals and corresponding frequency signals are shown.

Time domain | Frequency domain |
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Time domain | Frequency domain |
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Time domain | Frequency domain |
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1. Fast Fourier transform. Time signals are shown on the left. Assign the corresponding spectra on the right per drag & drop!

## Time domain

## Fequency domain