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Signed-off-by: David Rotermund <54365609+davrot@users.noreply.github.com>
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@ -19,5 +19,38 @@ y: np.ndarray = np.sin(t * 2 * np.pi * frequency_hz)
```
![figure 1](figure_1.png)
## Fourier transform with rfft
Since we deal with non-complex waveforms (i.e. only real values) we should use rfft. This is faster and uses less memory.
### 1 dimension
| | |
| ------------- |:-------------:|
| [numpy.fft.rfft](https://numpy.org/doc/stable/reference/generated/numpy.fft.rfft.html) | Compute the one-dimensional discrete Fourier Transform for real input. |
| [numpy.fft.irfft](https://numpy.org/doc/stable/reference/generated/numpy.fft.irfft.html) | Computes the inverse of [rfft](https://numpy.org/doc/stable/reference/generated/numpy.fft.rfft.html#numpy.fft.rfft). |
| [numpy.fft.rfftfreq](https://numpy.org/doc/stable/reference/generated/numpy.fft.rfftfreq.html) | Return the Discrete Fourier Transform sample frequencies (for usage with rfft, irfft). |
### 2 dimensions
| | |
| ------------- |:-------------:|
| [numpy.fft.rfft2](https://numpy.org/doc/stable/reference/generated/numpy.fft.rfft2.html) | Compute the 2-dimensional FFT of a real array. |
| [numpy.fft.irfft2](https://numpy.org/doc/stable/reference/generated/numpy.fft.irfft2.html) | Computes the inverse of rfft2. |
### N dimensions
| | |
| ------------- |:-------------:|
| [numpy.fft.rfftn](https://numpy.org/doc/stable/reference/generated/numpy.fft.rfftn.html) | Compute the N-dimensional discrete Fourier Transform for real input.
| [numpy.fft.irfftn](https://numpy.org/doc/stable/reference/generated/numpy.fft.irfftn.html) | Computes the inverse of rfftn.
Since we deal with a 1 dimensional time series
```python
y_fft: np.ndarray = np.fft.rfft(y)
frequency_axis: np.ndarray = np.fft.rfftfreq(y.shape[0]) * sampling_frequency
```