73 lines
2 KiB
Markdown
73 lines
2 KiB
Markdown
# Remove a common signal from your data
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## Goal
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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)
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Questions to [David Rotermund](mailto:davrot@uni-bremen.de)
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## Creating dirty test data
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```python
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import numpy as np
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import matplotlib.pyplot as plt
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rng = np.random.default_rng()
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time_series_length: int = 1000
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number_of_channels: int = 100
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t: np.ndarray = np.arange(0, time_series_length) / 1000
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# Clean data
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frequencies = 10 / rng.random((1, number_of_channels))
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phase = 2 * np.pi * rng.random((1, number_of_channels))
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clean_data: np.ndarray = (
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0.5
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* rng.random((1, number_of_channels))
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* np.sin(t[..., np.newaxis] * 2 * np.pi * frequencies + phase)
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+ np.arange(0, number_of_channels)[np.newaxis, ...]
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)
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# Perturbation
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y: np.ndarray = np.sin(t * 2 * np.pi * 1)
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mix_coefficients: np.ndarray = 1 + rng.random((number_of_channels)) * 5
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perturbation: np.ndarray = y[..., np.newaxis] * mix_coefficients[np.newaxis, ...]
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# Dirty data
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dirty_data: np.ndarray = clean_data.copy()
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dirty_data += perturbation
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np.savez(
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"data.npz", clean_data=clean_data, perturbation=perturbation, dirty_data=dirty_data
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)
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plt.plot(t, clean_data[..., 0:3])
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plt.xlabel("Time [s]")
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plt.ylabel("Clean data waveform")
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plt.show()
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plt.plot(t, perturbation[..., 0:3])
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plt.xlabel("Time [s]")
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plt.ylabel("Perturbation ")
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plt.show()
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plt.plot(t, dirty_data[..., 0:3])
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plt.xlabel("Time [s]")
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plt.ylabel("Dirty data ")
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plt.show()
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```
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We get three fully random time series
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Sine wave with random amplitudes as common perturbation
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Both combined with random mixing coefficients
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## Estimating the common signal
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