# Short-time Fourier transform

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The **short-time Fourier transform (STFT)** is a spectral decomposition method that involves calculating the Fourier transform of a windowed portion of a time-varying signal as the window slides down the time axis.

## Definition

The STFT requires a windowed portion of the signal, such that

where is the original signal and is the window function centered at time . The Fourier transform is computed for the windowed portion, for each , as follows:

- .
^{[1]}

The result is a representation of the one-dimensional signal in a two-dimensional time-frequency domain.

## References

- ↑ Cohen, L., 1995, Time-Frequency Analysis: Prentice-Hall