## 3 Experiment
Fast Fourier Transform was then applied to each window, resulting in a vector of power of spectrum \(\mathbf{X}=\left[X_{1},X_{2},\ldots,X_{\frac{N}{2}}\right]\) with a dimension of N/2 = 50. Here, each \(X_{k}\) represents the spectrum power at a frequency of \(k\times F_{1}\), with \(F_{1}\) = 4 Hz as the fundamental frequency. Figure 8 provides examples of the normalized Fourier spectrum analysis of the signals obtained from the flame and UVB lamp. The Fourier spectrum analysis results of the flame, as observed in this study, were observed to exhibit significant variability over time, indicating that the signal feature space may be difficult to model using standard techniques. To address this challenge, constructing distributions for the vector of spectrum power X was considered as a viable solution to the classification problem. Specifically, the Fourier spectrum amplitude values for each frequency over time were treated as random variables, and the joint probability distribution for these values was constructed. In this case, the input features were the Fourier spectrum amplitude values for each frequency, and the classification models were used to classify new signals as either coming from the flame or the UVB lamp. Due to the fact that the data that needs to be classified currently has exactly two classes, it is implied that the classification can be done with the Support Vector Machine (SVM) method, which is suitable for edge devices [12]. The advantages of this method can be listed as follows: it is effective in high-dimensional spaces, even in the cases where number of dimensions is greater than the number of samples; it is memory efficient due to the fact that it uses a subset of training points in the decision function; it offers flexibility in various kernel selection. In this work, the idea comes with using SVM for binary classification in which the data is labeled with \(y=1\) for the flame and \(y=-1\) for the UBV lamp. The aim of this method is to find the function of a hyperplane over the feature vector \(X\), which is the vector of spectrum power in this work:  
\[f(X)=X^{T}\beta+b \tag{1}\]  
Hence, it is necessary to specify the parameters \(\beta,b\) that must meet certain criteria. In practical, our data appears to not allow for a separating hyperplane. Therefore, the objective function to estimate \(\beta,b\) in this work presents the L\({}^{1}\)-norm problem, which is constructed by adding slack variables \(\xi_{j}\) and a penalty parameter \(C\), as follows:  
\[\min_{\beta,b,\xi_{j}}\left(\frac{1}{2}\beta^{T}\beta+C\sum_{j}\xi_{j}^{1}\right) \tag{2}\]  
Figure 3:0 Normalized Fourier spectrum analysis results for the output signals of a flame (**a**) and UV lamp (**b**). subjected to the constraints:  
Figure 3:1  
On the other hand, it was possible to capture the inherent variability of the flame signal over time and encode this information into a probabilistic model. This approach allowed for the development of a Naive Bayes model, which is a type of probabilistic classifier that assumes the independence of the input features. Overall, this approach proved to be effective at accurately distinguishing between these two types of signals and may be useful in other applications where signal variability poses a challenge to traditional classification techniques. The Naive Bayes classifier is typically used when predictors are independent of each other within each class. However, it has been shown to perform well in practice even when the independence assumption is not valid. Specifically, the Naive Bayes model estimated the probability density of predictor \(X\) (the vector of spectrum power) given class y-(flame or UVB lamp), denoted by \(P(X\,|\,y)\).