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Signed-off-by: David Rotermund <54365609+davrot@users.noreply.github.com>
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# [FFT](https://numpy.org/doc/stable/reference/routines.fft.html)
{:.no_toc}
<nav markdown="1" class="toc-class">
* TOC
{:toc}
</nav>
## The goal
Fouriert transformations are an important part of data analysis.
Questions to [David Rotermund](mailto:davrot@uni-bremen.de)
## [Numpy](https://numpy.org/doc/stable/reference/routines.fft.html) vs [scipy](https://docs.scipy.org/doc/scipy/tutorial/fft.html#fourier-transforms-scipy-fft)
```shell
pip install scipy
```
Numpy says [itself](https://numpy.org/doc/stable/reference/routines.fft.html#discrete-fourier-transform-numpy-fft):
> The SciPy module scipy.fft is a more comprehensive superset of numpy.fft, which includes only a basic set of routines.
```python
```
## [Discrete Fourier Transform (numpy.fft)](https://numpy.org/doc/stable/reference/routines.fft.html#discrete-fourier-transform-numpy-fft)
## [Standard FFTs](https://numpy.org/doc/stable/reference/routines.fft.html#standard-ffts)
|||
|---|---|
|[fft(a[, n, axis, norm])](https://numpy.org/doc/stable/reference/generated/numpy.fft.fft.html#numpy.fft.fft)|Compute the one-dimensional discrete Fourier Transform.|
|[ifft(a[, n, axis, norm])](https://numpy.org/doc/stable/reference/generated/numpy.fft.ifft.html#numpy.fft.ifft)|Compute the one-dimensional inverse discrete Fourier Transform.|
|[fft2(a[, s, axes, norm])](https://numpy.org/doc/stable/reference/generated/numpy.fft.fft2.html#numpy.fft.fft2)|Compute the 2-dimensional discrete Fourier Transform.|
|[ifft2(a[, s, axes, norm])](https://numpy.org/doc/stable/reference/generated/numpy.fft.ifft2.html#numpy.fft.ifft2)|Compute the 2-dimensional inverse discrete Fourier Transform.|
|[fftn(a[, s, axes, norm])](https://numpy.org/doc/stable/reference/generated/numpy.fft.fftn.html#numpy.fft.fftn)|Compute the N-dimensional discrete Fourier Transform.|
|[ifftn(a[, s, axes, norm])](https://numpy.org/doc/stable/reference/generated/numpy.fft.ifftn.html#numpy.fft.ifftn)|Compute the N-dimensional inverse discrete Fourier Transform.|
## [Real FFTs](https://numpy.org/doc/stable/reference/routines.fft.html#real-ffts)
|||
|---|---|
|[rfft(a[, n, axis, norm])](https://numpy.org/doc/stable/reference/generated/numpy.fft.rfft.html#numpy.fft.rfft)|Compute the one-dimensional discrete Fourier Transform for real input.|
|[irfft(a[, n, axis, norm])](https://numpy.org/doc/stable/reference/generated/numpy.fft.irfft.html#numpy.fft.irfft)|Computes the inverse of rfft.|
|[rfft2(a[, s, axes, norm])](https://numpy.org/doc/stable/reference/generated/numpy.fft.rfft2.html#numpy.fft.rfft2)|Compute the 2-dimensional FFT of a real array.|
|[irfft2(a[, s, axes, norm])](https://numpy.org/doc/stable/reference/generated/numpy.fft.irfft2.html#numpy.fft.irfft2)|Computes the inverse of rfft2.|
|[rfftn(a[, s, axes, norm])](https://numpy.org/doc/stable/reference/generated/numpy.fft.rfftn.html#numpy.fft.rfftn)|Compute the N-dimensional discrete Fourier Transform for real input.|
|[irfftn(a[, s, axes, norm])](https://numpy.org/doc/stable/reference/generated/numpy.fft.irfftn.html#numpy.fft.irfftn)|Computes the inverse of rfftn. |
## [Hermitian FFTs](https://numpy.org/doc/stable/reference/routines.fft.html#hermitian-ffts)
|||
|---|---|
|[hfft(a[, n, axis, norm])](https://numpy.org/doc/stable/reference/generated/numpy.fft.hfft.html#numpy.fft.hfft)|Compute the FFT of a signal that has Hermitian symmetry, i.e., a real spectrum.|
|[ihfft(a[, n, axis, norm])](https://numpy.org/doc/stable/reference/generated/numpy.fft.ihfft.html#numpy.fft.ihfft)|Compute the inverse FFT of a signal that has Hermitian symmetry.|
## [Helper routines](https://numpy.org/doc/stable/reference/routines.fft.html#helper-routines)
|||
|---|---|
|[fftfreq(n[, d])](https://numpy.org/doc/stable/reference/generated/numpy.fft.fftfreq.html#numpy.fft.fftfreq)|Return the Discrete Fourier Transform sample frequencies.|
|[rfftfreq(n[, d])](https://numpy.org/doc/stable/reference/generated/numpy.fft.rfftfreq.html#numpy.fft.rfftfreq)|Return the Discrete Fourier Transform sample frequencies (for usage with rfft, irfft).|
|[fftshift(x[, axes])](https://numpy.org/doc/stable/reference/generated/numpy.fft.fftshift.html#numpy.fft.fftshift)|Shift the zero-frequency component to the center of the spectrum.|
|[ifftshift(x[, axes])](https://numpy.org/doc/stable/reference/generated/numpy.fft.ifftshift.html#numpy.fft.ifftshift)|The inverse of fftshift.|