Add Stream.filter to filter signals from the stream

[mscheltienne]

Stream filter API should allow:

stream = StreamLSL(...).connect()
stream.filter(1., 100., picks="eeg")
stream.filter(1., 15., picks="ecg")
stream.notch_filter(np.arange(50, 150, 50), picks="all")

In practice, we have:

• a ringbuffer of shape (n_samples, n_channels), already processed (re-referenced, filter, ..)
• a new chunk of data of shape (n_samples, n_channels), raw

The API should support:

• different filters applied to different channels -> how do we handle the delay introduced by the different filters?
• more than one filter applied to a given channel -> does the order matter?

[mscheltienne]

@larsoner I would like to start looking into this one, I remember you mentioned scipy functions to efficiently work on ringbuffer. Would you have some references or hints I could look into?

[larsoner]

For realtime applications I would expect an IIR filter with scipy.signal.sosfilt to work reasonably well. Filter a given buffer, save the end filter states, next buffer you filter pass those to sosfilt, etc. and it's the same as filtering one long continuous signal instead of individual buffers. (And sosfilt is more stable than lfilter for higher filter orders.) Here's a tiny snippet I used once:

        if self._zi is None:
            self._zi = sosfilt_zi(sos)[:, :, np.newaxis] * data[:, :1].T
        data[:], self._zi = sosfilt(sos, data, zi=self._zi)

[mscheltienne]

Great, that's similar to what I added a couple of years ago to the current viewer:

mne-lsl/mne_lsl/stream_viewer/scope/scope_eeg.py

Lines 122 to 128 in 9515159

	if self._zi is None:
	logger.debug("Initialize ZI coefficient for BP.")
	# Multiply by DC offset
	self._zi = self._zi_coeff * np.mean(self._data_acquired, axis=0)
	self._data_acquired, self._zi = sosfilt(
	self._sos, self._data_acquired, 0, self._zi
	)

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I just re-read the background on filtering tutorial, and IMO, if someone wants to apply 2 different filters to 2 different channels within the Stream, it falls upon him to handle the difference in filter response. Do you agree or do you think we should prevent some combinations/parameters (order, transition bandwidth, ..)?

In the case of 2 different filters applied to 2 different channels, is it possible to combined the sos and zi to then run a single call through sosfilt or should we split those?

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Same questions in the case of 2 different filters applied to the same channels, e.g. bandpass (1, 100) Hz + notch (50, 100) Hz, can we combine the coefficients and call sosfilt only once?

[larsoner]

Do people want different filtering on different channels? If they do in principle then I would from the start plan on having N different filters each with a set of picks, coefficients, and filter states. Iterating over the N shouldn't be too painful (N will probably never be greater than 10 or so, and only in the thousands would I expect Python call overhead to start to matter.)

Same questions in the case of 2 different filters applied to the same channels, e.g. bandpass (1, 100) Hz + notch (50, 100) Hz, can we combine the coefficients and call sosfilt only once?

For this you can, yeah. SOS is really a way of turning say a 10th order filter into 5 2nd order filters, then (by linearity) equivalently filtering sequentially rather than all at once, which is more numerically stable. So if you have multiple SOS filters you can just concatenate the coefficients and it should work.