# Determining where filter-hilbert data contains a signal

I’m using filter-hilbert to get frontal lobe frequency data and it works great with the left hemisphere, but it’s pretty spotty with the right hemisphere, probably because of how the left hemisphere bulges in the front while the right hemisphere bulges in the rear, so some spots on the head have a strong signal while others don’t. Is there a good way to determine where and when filter-hibert data contains a signal?. Off the top of my head, I’ve been trying taking the average bin values for the relevant band from a STFFT and comparing them to the max bin value and trying to find a good threshold ratio between the two, but that’s pretty subjective, and I’m curious if there is a better way, especially since that is based on a windowed STFFT while the filter-hilbert data is a continuous analytic signal.

Good question, Steve. I think there are two approaches:

1. Repeat the analysis for lots of frequency bands and then show the results over the spectrum, or time-frequency spectrum depending on what you’re doing with the analyses.
2. Use an FFT or Welch’s method to identify peaks in the spectrum, and then filter-Hilbert at those peaks.

In fact, these two methods aren’t so different from each other; essentially the idea is to pick some frequency range based on the characteristics of the data, which are either (1) the thing you’re looking for, or (2) spectral power.

Thanks Mike,
#2 is how I figured out the range to bandpass filter (I’m examining the theta range). The frequency is very non-stationary, moving between 7hz and 8hz, so I’m not sure #1 will help. Since the EMG is a broadband signal while the theta is a narrowband signal, is there any way to use the power/phase/frequency information from the bandpass filtered analytic signal to judge whether the broadband or narrowband signal predominates?

I wouldn’t call moving between 7 and 8 Hz “very non-stationary” – that actually seems a bit on the narrow side for neural oscillations. It’s also more narrow than typical filter bandwidths.

Regarding the integration with EMG, there is, of course, narrowband corticomuscular coherence in theta and beta. So there are narrowband features that are embedded in the broadband EMG response. I suppose you could try a cross-frequency-coupling type of analysis where you see whether EMG (broadband) energy is concentrated at particular theta phases. Is that what you meant?

I don’t think that’s quite what I meant, I’m basically looking for a way to do a signal to noise ratio where the narrowband theta is the signal and the broadband EMG is the noise.

Ah, I see. In the SSVEP literature, people sometimes compute the spectral SNR, which is power at each frequency divided by average power in the neighboring frequencies, excluding a bit for the non-stationarities. For example, SNR at 10 Hz could be defined as power at 10 Hz divided by power averaged between 5-9 Hz and 11-15 Hz. Then you apply that sliding window across the spectrum. It’s conceptually similar to running a high-pass filter through the power spectrum, in that the sluggish trends including the 1/f will tend to 1, whereas narrow peaks will be accentuated.

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It would be great if it were feasible to tell just from the analytic signal, shouldn’t it be possible to figure out whether the signal is narrowband or broadband just based on the variance of the instantaneous frequencies?

hmm, that’s an interesting thought. Certainly you can average the power time series from the analytic signal – that ends up being essentially Welch’s method when looking across the spectrum.

However, the phase of the analytic signal (from which instantaneous frequency is computed) is independent of the amplitude, so I think the variability would tell you more about the stability of an oscillation than its amplitude per se. I guess if it’s just filtered noise you would expect the variability to be higher. But it also depends on the filter bandwidth… Eric Maris’ group had a paper that is relevant to your question: https://www.sciencedirect.com/science/article/abs/pii/S1053811915004796?via%3Dihub