# Automating Stimulation Frequency Selection for SSVEP-Based Brain-Computer Interfaces
## 5 Experimental Evaluation
### Coefficients Analysis Application
And if the user needs the fastest response to a stimulus, then it is possible to set the \(K_{sp}\) coefficient threshold close to one, and slightly decrease the \(K_{o}\) coefficient threshold. In cases where there are strict requirements for response speed and SNR threshold overshoot, both thresholds of these coefficients can be set closer to one, although this may significantly reduce the final list of recommended frequencies. The application also includes the ability to set minimum values for the three \(K_{fa}\) coefficients. The proximity of these coefficients to one depends heavily on the values of the \(K_{sp}\) and \(K_{o}\) coefficients. Therefore, setting the minimum allowable values for the \(K_{fa}\) coefficients ensures that the mutual influence of the \(K_{sp}\) and \(K_{o}\) coefficients will not result in the application selecting a frequency with a maximum value for one coefficient at the expense of significantly reducing the other. Instead, the application will maintain a balance between the values of the \(K_{sp}\) and \(K_{o}\) coefficients by selecting stimulation frequencies that best satisfy the established thresholds for the \(K_{sp}\), \(K_{o}\), and \(K_{fa}\) coefficients simultaneously. In this case, only the threshold coefficient \(K_{fa}\) with the maximum value will be considered for each photostimulus frequency. As a result, the list of recommended frequencies will also indicate which \(K_{fa}\) coefficient formula should be used to detect SSVEP potential at a given photostimulus frequency. This allows us to additionally consider stimulation frequencies where the SSVEP potential is exclusively present at the main or multiple stimulation frequencies. Additionally, this approach takes into account different time delays or response stabilities at the main and multiple frequencies, selecting the best option. Considering these factors expands the final list of recommended frequencies. The process of selecting recommended frequencies in our application was designed in such a way that the first priority is given to searching for stimulation frequencies that exceed the threshold value of the \(K_{fa}(f,2f)\) coefficient. This ensures that the list primarily includes frequencies that produce a high response at both the main and multiple stimulation frequencies. The remaining frequencies are then selected in descending order of the values of the \(K_{fa}(f)\) and \(K_{fa}(2f)\) coefficients, which are analyzed as a unified list. This approach allows us to properly take into account those subjects who are most characterized by SSVEP potentials occurring at multiple stimulation frequencies rather than at the main stimulation frequencies. Finally, the user can set the maximum allowable discomfort coefficient \(K_{d}\) as the last threshold value. This allows the list of recommended frequencies to be adjusted by excluding frequencies that cause discomfort for the subject. For example, as shown in Figure 9, our application excluded the frequency of photostimulation at 17 Hz from the list of recommended frequencies due to its high discomfort coefficient. However, this frequency passed all other threshold values set for the \(K_{sp}\), \(K_{o}\), and \(K_{fa}\) coefficients. It is important to note that because SSVEP potentials can arise not just at the primary frequency but also at its multiples, some chosen frequencies might be mathematically incompatible. For example, the photostimuli presentation with a frequency of 5 and 10 Hz in both cases can provoke a reaction at 10 Hz, 20 Hz, etc. This feature is not taken into account in our application because its primary goal is to generate the most complete list of potentially usable frequencies.