The electromagnetic wave is analyzed through the Fourier transformation, though it has a limitation of the resolution.
The Fourier transforms the wave to a mathematical formula, whose methodology is imperfect, though the mathematical approach is the only way to resolve it. When the wave consists of the sole frequency, it is unnecessary to be cracked, though when composed of the multiple frequencies, each frequency cannot be identified until transformed in this way.
This is a critical issue to the brainwave, as it is quite less likely composed by the single frequency, rather created by the multiple chemical changes and frequencies, which requires the Fourier transformation. However, its methodology has a limitation at the resolution and sampling rate. If the wave is necessary to be analyzed at the exact frequency, the original wave should be recorded in a long time, otherwise the analysis becomes quite rough. It means the wave can be analyzed at 10Hz unit frequency for the shorter recorded wave, which is quite problematic to the brainwave, as it originally just irradiates up to 100Hz wavelength.
If the brainwave keeps the same frequency pattern for a long time, the analysis gets deeper into the minute. When the certain stimulus is given to the subject for a long time without any other stimulation and thinking, the brainwave is resolved to the minute frequencies, but it is apparently not a normal condition. It is not impossible to experiment in this way, but impractical to the brainwave control on the normal occasion.
Fast Fourier Transformation is its extension to solve an issue of the resolution, which also requires the wave with a longer time, though it can define the frequency irradiated at each segmented time. This is one of the solutions but still limited at the level of its resolution. It can be analyzed at 1Hz unit, but maybe hard to analyze the level at the second decimal.
There is another practical issue to this methodology, which is a difficulty at the feedback to use the outcome to affect the subject. The past data or recorded brainwave can be analyzed in this manner, though it requires many calculations with many variables. It means it is impossible to solve it instantaneously for the feedback even with the super computer.
All in all, the digital analysis of the brainwave is not progressed that much due to its limitation. The difficulty is not at an external replication of the brainwave by digital, but at the digital analysis.
However, there is a way to understand the meaning of the brainwave without these analyses.