Update README.md

Signed-off-by: David Rotermund <54365609+davrot@users.noreply.github.com>

SVD_data_cleaning/README.md

@@ -1 +1,54 @@
+# Remove a common signal from your data
+## Goal
+We want to remove a common signal which was mixed on top a set of data channels. There are many methods to do so. We will use SVD. Implementations are for example: [scipy.linalg.svd](https://docs.scipy.org/doc/scipy/reference/generated/scipy.linalg.svd.html) or [torch.svd_lowrank](https://pytorch.org/docs/stable/generated/torch.svd_lowrank.html) (which also works on the GPU)
 
+Questions to [David Rotermund](mailto:davrot@uni-bremen.de)
+
+## Creating dirty test data 
+
+```python
+import numpy as np
+import matplotlib.pyplot as plt
+
+rng = np.random.default_rng()
+
+time_series_length: int = 1000
+number_of_channels: int = 3
+
+# Clean data
+clean_data: np.ndarray = (
+    rng.random((time_series_length, number_of_channels))
+    + 5 * np.arange(0, number_of_channels)[np.newaxis, ...]
+)
+
+# Perturbation
+t: np.ndarray = np.arange(0, time_series_length) / 1000
+y: np.ndarray = np.sin(t * 2 * np.pi * 1)
+mix_coefficients: np.ndarray = 1 + rng.random((3))
+perturbation: np.ndarray = y[..., np.newaxis] * mix_coefficients[np.newaxis, ...]
+
+# Dirty data
+dirty_data: np.ndarray = clean_data.copy()
+dirty_data += perturbation
+
+np.savez(
+    "data.npz", clean_data=clean_data, perturbation=perturbation, dirty_data=dirty_data
+)
+
+plt.plot(t, clean_data)
+plt.xlabel("Time [s]")
+plt.ylabel("Clean data waveform")
+plt.show()
+
+plt.plot(t, perturbation)
+plt.xlabel("Time [s]")
+plt.ylabel("Perturbation ")
+plt.title("Perturbation waveform")
+plt.show()
+
+plt.plot(t, dirty_data)
+plt.xlabel("Time [s]")
+plt.ylabel("Perturbation ")
+plt.title("Dirty data waveform")
+plt.show()
+```