Note

Click here to download the full example code

# Compute a cross-spectral density (CSD) matrix¶

A cross-spectral density (CSD) matrix is similar to a covariance matrix, but in the time-frequency domain. It is the first step towards computing sensor-to-sensor coherence or a DICS beamformer.

This script demonstrates the three methods that MNE-Python provides to compute the CSD:

Using short-term Fourier transform:

`mne.time_frequency.csd_fourier()`

Using a multitaper approach:

`mne.time_frequency.csd_multitaper()`

Using Morlet wavelets:

`mne.time_frequency.csd_morlet()`

```
# Author: Marijn van Vliet <w.m.vanvliet@gmail.com>
# License: BSD (3-clause)
from matplotlib import pyplot as plt
import mne
from mne.datasets import sample
from mne.time_frequency import csd_fourier, csd_multitaper, csd_morlet
print(__doc__)
```

Out:

```
```

In the following example, the computation of the CSD matrices can be
performed using multiple cores. Set `n_jobs`

to a value >1 to select the
number of cores to use.

```
n_jobs = 1
```

Loading the sample dataset.

```
data_path = sample.data_path()
fname_raw = data_path + '/MEG/sample/sample_audvis_raw.fif'
fname_event = data_path + '/MEG/sample/sample_audvis_raw-eve.fif'
raw = mne.io.read_raw_fif(fname_raw)
events = mne.read_events(fname_event)
```

Out:

```
Opening raw data file /home/circleci/mne_data/MNE-sample-data/MEG/sample/sample_audvis_raw.fif...
Read a total of 3 projection items:
PCA-v1 (1 x 102) idle
PCA-v2 (1 x 102) idle
PCA-v3 (1 x 102) idle
Range : 25800 ... 192599 = 42.956 ... 320.670 secs
Ready.
Current compensation grade : 0
```

By default, CSD matrices are computed using all MEG/EEG channels. When interpreting a CSD matrix with mixed sensor types, be aware that the measurement units, and thus the scalings, differ across sensors. In this example, for speed and clarity, we select a single channel type: gradiometers.

```
picks = mne.pick_types(raw.info, meg='grad')
# Make some epochs, based on events with trigger code 1
epochs = mne.Epochs(raw, events, event_id=1, tmin=0, tmax=1,
picks=picks, baseline=(None, 0),
reject=dict(grad=4000e-13), preload=True)
```

Out:

```
72 matching events found
Applying baseline correction (mode: mean)
Not setting metadata
3 projection items activated
Loading data for 72 events and 602 original time points ...
0 bad epochs dropped
```

Computing CSD matrices using short-term Fourier transform and (adaptive) multitapers is straightforward:

```
csd_fft = csd_fourier(epochs, fmin=15, fmax=20, n_jobs=n_jobs)
csd_mt = csd_multitaper(epochs, fmin=15, fmax=20, adaptive=True, n_jobs=n_jobs)
```

Out:

```
Computing cross-spectral density from epochs...
Computing CSD matrix for epoch 1
Computing CSD matrix for epoch 2
Computing CSD matrix for epoch 3
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[done]
Using multitaper spectrum estimation with 7 DPSS windows
Computing cross-spectral density from epochs...
Computing CSD matrix for epoch 1
Computing CSD matrix for epoch 2
Computing CSD matrix for epoch 3
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[done]
```

When computing the CSD with Morlet wavelets, you specify the exact frequencies at which to compute it. For each frequency, a corresponding wavelet will be constructed and convolved with the signal, resulting in a time-frequency decomposition.

The CSD is constructed by computing the correlation between the
time-frequency representations between all sensor-to-sensor pairs. The
time-frequency decomposition originally has the same sampling rate as the
signal, in our case ~600Hz. This means the decomposition is over-specified in
time and we may not need to use all samples during our CSD computation, just
enough to get a reliable correlation statistic. By specifying `decim=10`

,
we use every 10th sample, which will greatly speed up the computation and
will have a minimal effect on the CSD.

```
frequencies = [16, 17, 18, 19, 20]
csd_wav = csd_morlet(epochs, frequencies, decim=10, n_jobs=n_jobs)
```

Out:

```
Computing cross-spectral density from epochs...
Computing CSD matrix for epoch 1
Computing CSD matrix for epoch 2
Computing CSD matrix for epoch 3
Computing CSD matrix for epoch 4
Computing CSD matrix for epoch 5
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[done]
```

The resulting `mne.time_frequency.CrossSpectralDensity`

objects have a
plotting function we can use to compare the results of the different methods.
We’re plotting the mean CSD across frequencies.

```
csd_fft.mean().plot()
plt.suptitle('short-term Fourier transform')
csd_mt.mean().plot()
plt.suptitle('adaptive multitapers')
csd_wav.mean().plot()
plt.suptitle('Morlet wavelet transform')
```

**Total running time of the script:** ( 0 minutes 19.937 seconds)

**Estimated memory usage:** 230 MB