From f3de651428ee93d68869df3fb64b9212753b8487 Mon Sep 17 00:00:00 2001
From: David Rotermund <54365609+davrot@users.noreply.github.com>
Date: Thu, 16 Nov 2023 17:23:48 +0100
Subject: [PATCH] Update README.md

Signed-off-by: David Rotermund <54365609+davrot@users.noreply.github.com>
---
 numpy_fft_1/README.md | 35 ++++++++++++++++++++++++++++++++++-
 1 file changed, 34 insertions(+), 1 deletion(-)

diff --git a/numpy_fft_1/README.md b/numpy_fft_1/README.md
index 7440453..1c7e5e5 100644
--- a/numpy_fft_1/README.md
+++ b/numpy_fft_1/README.md
@@ -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
+```