Time-frequency and power spectra

Discussions
1

Dear Brainstorm community,

I need to have a clear understanding about aspects that are related to time-frequency, and power spectra, although I know that each of them is applied in different situations. Thus, I attached 2 plots that are generated from the same electrode of the same subject. First one is about time-frequency and the other one is about power spectra. You can see from the plot of power spectra, delta band has the highest power, while in the plot of time-frequency,beta band has the highest power. Therefore, my question, should the band that has the highest power in frequency domain to be the one that has the highest frequency in the time-frequency domain? In other words, should both plots have highest value for delta band, or it is not necessary?

Note: I used the defaults setting in both cases.

Thanks in advance.
John

2

Hi John,

The time-frequency plot you attached here does not show the power in a given frequency band: it has been normalized in some way and this normalization has been done for each frequency separately to bring all the values for all the frequencies in the same range. You should look at the non-normalized TF maps if you want to see similar effects and ranges of values.
In general, you should not be comparing the measure of power you obtain between different frequency bands, you will always observe larger power in the lower frequencies. You should measure deviations between subjects or conditions for one frequency band, or deviations between a latency of interest and a baseline level.

These two measures are not adapted to answer the same questions. If you are expecting the power in a certain frequency band to change over time, linked with a change in the subject state, then use a time-frequency decomposition.
If you are not interested in the timing or if you don’t have any hypothesis about the temporal evolution of the power in your frequency band of interest: compute a power spectrum.

Francois

3

Hi Francois,

Thanks for your answer.

1- Could you declare the Brainstorm options that give same results.

2- Based on what you said “You should look at the non-normalized TF maps if you want to see similar effects and ranges of values”. Could you refer to the option that provide “non-normalized TF maps if”.

Best,
John

4

  1. You cannot get the same results, they are different measures, and correspond to fundamentally different ways of looking at the data.
    The closest you could get to a power spectrum from a TF decomposition would be by averaging in time your TF maps.

  2. Do not select the option “1/f compensation” and do not apply any normalization after (Z-score or others).
    But this not the correct approach for exploring time-frequency representations… To be able to read the TF maps you need some for of normalization, and to make interesting observations most of the time you need to compute a deviation with respect to a control level.

5

I thought I can obtain same result using Brainstorm especially that I had the 2 plots from Brainstorm toolbox.

6

Hi John:

I agree with François: it is not a matter of consistency of outputs from different Brainstorm functions, it is a matter of what they actually represent. Please refer to his last comment and follow carefully his recommendations. If you do, you will then verify that the time-averaged time-frequency decomposition will have a similar profile as the power-spectrum density plot, if both are applied on the exact same data segments.

Hope this helps,

7

Hi Sylvain,

Thanks for your contribution. I’m sure that Francois is right. I’ll try to find the settings that Francois mentioned in order to solve this issue. Because as I said, I did not change the settings for both spectra and time-frequency in Brainstorm.

Regards,
John

8

Hi Francois , John, and Sylvain,

Due to your advice “should not be comparing the measure of power you obtain between different frequency bands, you will always observe larger power in the lower frequencies”, so you recommended “should measure deviations between subjects or conditions for one frequency band, or deviations between a latency of interest and a baseline level”.

Now, my question:

With applying “Multitaper” and then “Fast Fourier transform” can we solve the problem of having larger power in the lower frequencies, so we can compare different frequency bands without having any problem, or this doesn’t help?

Leonardo

9
  • “Having larger power in the lower frequencies” is not a “problem”, it’s just how the signals you are processing are.
  • If you want to normalize the power across frequencies before the time-frequency analysis, you can use the process “Pre-process > ARIMA filter” with the default options.
  • There is no multitaper process available in Brainstorm - and it would a replacement for the FFT, not a precedent step
  • In the first place: Are you sure you need the time dimension of the time-frequency analysis? Why don’t you just use the Welch’s PSD estimate?
    => The method you use depends mostly on the questions you have… If you don’t have a clear hypothesis to test on your data, you will not be able to build the appropriate analysis pipeline.
10

Also Leonardo, please note that lesser power in higher frequency bands is an intrinsic property of the electrophysiological signals; not an artefact of the spectral analysis methods. Normalization across frequencies is a secondary step in the analysis, essentially for visualization purposes.