[BUG] Cross-spectral density missing frequencies

[tsbinns]

Reference issue

Discussed in call with @larsoner & @wmvanvliet.

What does this implement/fix?

Currently, computing the CSD with the csd_multitaper, csd_fourier, csd_array_multitaper, or csd_array_fourier functions of the time_frequency module will return a CrossSpectralDensity object whose frequencies do not match the fmin and fmax parameters supplied to the functions.

E.g. calling the functions with fmin=5, fmax=10 could be expected to return a CSD object with frequencies [5, 6, 7, 8, 9, 10] (assuming a 1 Hz resolution). Instead, the following frequencies are returned [6, 7, 8, 9].

This occurs because of the logic used to generate the internal frequency mask:

orig_frequencies = rfftfreq(n_fft, 1.0 / sfreq)
freq_mask = (orig_frequencies > fmin) & (orig_frequencies < fmax)

As such, the fmin and fmax entries of 5 and 10 Hz may be included in the list of possible frequencies, but they are ignored when generating the frequency mask (e.g. as 5 is not greater than itself, and 10 is not less than itself).

A simple solution if to allow entries of orig_frequencies to also match fmin and fmax, e.g.:

mne-python/mne/time_frequency/csd.py

Lines 814 to 816 in 74e7348

	freq_mask = (
	(orig_frequencies > 0) & (orig_frequencies >= fmin) & (orig_frequencies <= fmax)
	)

This change ensures that fmin=5, fmax=10 will return a CSD object with frequencies [5, 6, 7, 8, 9, 10]. Note that (orig_frequencies > 0) is important to prevent the CSD being returned for the zero frequency, which would not match the behaviour of other spectral methods (e.g. PSD computation).

@larsoner This does not include logic for cases that can be considered as floating point errors, but if I recall you said this was optional.

This requires a small change to the unit tests for catching failing cases where no frequency bins are captured due to fmin and fmax being too close, e.g.:
https://github.com/tsbinns/mne-python/blob/74e7348be7536b42bca2fa3ce48ecd4f0536a89b/mne/time_frequency/tests/test_csd.py#L397

[mscheltienne]

Great explanation in this PR, thank you!

[larsoner]

Just tacking on a little test here...

@meeseeksdev Hello

[lumberbot-app]

Look at me, @larsoner, I'm Mr. Meeseeks!

[larsoner]

@meeseeksdev backport to maint/1.7