[Eeglablist] Which is the best way to measure the "alpha" oscillation?

[Евгений Машеров]

My comment is twofold. On the one hand, it answers a specific question: why do different authors indicate different subrange boundaries, even though they are approximately equal? ​​This is because different calculation methods, depending on the sampling rate and epoch length, as well as the presence of a weighting function and other factors, yield different "frequency combs."
On the other hand, I would like to draw attention to the uncertainty principle in signal processing (which is not the same as the uncertainty principle in quantum physics, but is deeply related to it, since both follow from the uncertainty principle in harmonic analysis). This principle asserts that it is impossible to accurately determine the frequency from a finite-length signal segment. By abandoning the fast Fourier transform in favor of the computationally wasteful general form of the discrete Fourier transform, we can use any frequency comb, including a non-uniform one, but the error remains. By lengthening the epoch, we can increase the accuracy of the frequency spectrum estimation, but here the variability of the state of the living organism begins to influence, which also affects the frequency characteristics, so absolute accuracy is unattainable.

> Eugen -
> 
> You are correct in saying that the band*width* of a spectral measure
> depends on the length of the spectral window you use - and (for frequencies
> near the half-sampling_rate Nyquist frequency) on the frequency resolution
> of the signal -- as well as on the spectral measure you are using (you
> mention FFT). The FFT was a great advance in spectral measurement when
> computers were (relative to today) very slow, as it made spectral analysis
> practical in many circumstances. That is no longer the case for typical
> applications in offline analysis of EEG. Thus, the EEGLAB time/frequency
> function does not need to use FFTs (*Fast* Fourier Transforms) computing at
> a limited set of frequencies (N/window_length, N=1,2,3,...), but rather,
> Fourier transforms at whatever set of center frequencies you wish (equally
> or log spaced, etc.).
> 
> What is of interest for this thread are differences in exact central
> frequencies of alpha bursts. If you have spectral measurements across
> (e.g.) trials or bursts, you can build a distribution of central
> frequencies, and then develop statistical margin of error measures that
> could distinguish alpha central frequencies with any degree of resolution
> (even 0.1 Hz or less), given enough data.
> 
> In particular, Independent Modulator Analysis (IMA), in 'learning from the
> data' to account for its log spectral power variations across time as a sum
> of activities in a set of fixed spectral bands (the Independent Modulators
> or IMs), can find central frequencies for each IM peak with quite high
> resolution (depending on data length, homogeneity, etc.).
> 
> Scott
> 
> On Thu, Apr 30, 2026 at 10:11 AM Евгений Машеров via eeglablist <
> eeglablist at sccn.ucsd.edu> wrote:
> 
>> It seems to me that there is no single, task-independent way to describe
>> the alpha rhythm. Dividing it into subranges is justified in some cases.
>> For example, it has been proposed to distinguish three subranges:
>> Alpha-1 (low frequency): ~7.7–9.2 Hz (sometimes defined as 8–9 Hz or 8–10
>> Hz). Associated with relaxation processes and often predominates during
>> decreased cognitive activity or in certain pathological conditions.
>> Alpha-2 (mid frequency): ~9.3–10.5 Hz (often 10–11 Hz). Reflects active,
>> quiet wakefulness.
>> Alpha-3 (high frequency): ~10.6–12.9 Hz (often 12–13 Hz). Associated with
>> sensory and cognitive attention processes, functionally closer to the beta
>> rhythm.
>>
>> However, specifying their boundaries with an accuracy of tenths of a hertz
>> may be related to processing features, including the sampling frequency and
>> the number of points in the Fourier transform. For example, with a sampling
>> frequency of 500 Hz and 1024 FFT points, the frequency step will be 0.488
>> Hz, meaning specifying them more accurately than half a hertz is pointless.
>> However, if 4096 FFT points are used with the same sampling frequency, the
>> step will be 0.122 Hz. Using window functions results in a blurring of the
>> spectral peaks and a widening of the range boundaries. This can lead to
>> incompatibility between data recorded under different conditions and
>> processed with different algorithms. Additional uncertainty is introduced
>> by the possibility of using total power or peak power, the average
>> frequency over the range, or the frequency of the most pronounced peak.
>> I believe that different approaches should be used for different classes
>> of problems, but a single approach should be used within a single class of
>> problems whenever possible.
>>
>> Your truly
>>
>> Eugen Masherov
>>