# How do you compare the amplitudes of different frequencies?

• Tristan Sguigna
In summary, the wider the frequency band, the larger the amplitude. This is difficult to compare statistically because the amplitude of a wider band is generally larger than the amplitude of a narrower band.f

#### Tristan Sguigna

Hello everyone! I am in a pickle right now as I attempt to move forward in my research project on neurofeedback. I am trying to calculate the theta/beta ratio for individual subjects and then compare them statistically. The issue I am having is statistically comparing amplitudes of different frequency bands. For example, in the theta category, I have a subject that had his/her frequency range of 2-9 Hz inhibited. For another subject, his/her frequency range of 3-6 Hz was inhibited. I cannot compare the average amplitudes of these two subjects because the wider a frequency band is, the larger the amplitude is (generally). Basically, for the first subject, what would his/her amplitude be if I restricted the bandwidth from 2-9 Hz to 3-6 Hz? The average amplitude for the 2-9Hz range is 34.3, so how much would the average amplitude decrease by if I restricted that subject's frequency range to 3-6 Hz? Let me know if this issue is not clear and I will try to adjust my question. Thanks everybody!

Do you have any theory or data that supports your belief that the average amplitude decreases as the range decreases? With no theory or data, I don't see how anyone can help you.

Dear FactChecker,

I appreciate your inquiry into my issue. Perhaps it will help if i give you context for my question. Here it is below:

I am measuring the power (amplitude) of a subject’s brain wave by itself and also within certain frequency bands during neurofeedback sessions. I already have all of the data recorded. The research subject would come into the clinic; I would measure the amplitude of a raw brain wave signal for 30 minutes at a certain location of the subject’s brain (such as the frontal cortex for an example). At the top of the screen display would be the raw wave signal of the frontal cortex. Below the raw signal would be 3 different brain wave signals filtered from the same top raw signal. These 3 different signals are filtered from the raw signal by different frequency ranges. So at the top of the display screen would be the raw EEG signal of the frontal cortex. Below this raw signal would be one brain wave signal (part of the same raw signal) at the frequency of 2-9 Hz. Below that signal would be another brain wave signal (part of the same raw signal) at 12-15 Hz. Below that signal would be the last brain wave signal (once again, part of the raw signal) at 22-36 Hz. Therefore, at the end of the 30 minute recording, I would have average amplitudes for the subject’s brainwave from the frontal cortex at 2-9 Hz (amplitude=34.3 microvolts), at 12-15 Hz (amplitude=9.8 microvolts), and at 22-30 Hz (amplitude=7.6 microvolts). The amplitude of the raw signal at the top of the screen display is always much greater than any of these amplitudes (raw signal amplitude averages around 70 microvolts). Hopefully this explains your question. I know amplitude usually doesn't relate to frequency, but as I mentioned above, the amplitude of the raw brain wave signal is always much greater than the amplitude of the filtered signals from the raw signal. Therefore, increasing the frequency range generally leads to higher amplitude levels. Thank you for your help.

It depends very much on the filter transfer function processing your signals. Filters can have sharper or softer attenuation beyond their passband frequencies depending on the filter design.

Unless you can determine the filter characteristic transfer function you won't be able to answer your question except empirically, using known signal frequencies spread from 2-9 Hz in your example.

FactChecker
Can you test the filter response to a known input? The filter response to a frequency sweep of known amplitude would help. Otherwise, if you have some data or specifications for the filter, that would be helpful.