## 3 Results and Discussion
### Case of Non-Parametric Analysis
This behavior can be attributed to the continuous electrical activity in the tissues of the plants, likely related to water and nutrient transport processes, as well as electrophysiological responses to external stimuli or the stress induced by the measurement setup. Additionally, the noise introduced by the electronic system is considered a contributing factor. These observations highlighted the need for digital signal processing techniques, such as the wavelet transform and AR Model, to analyze the signals effectively. To further validate the consistency across the 15 signals, the cosine similarity coefficient was calculated defined by Equation (4). \[\text{Cosine Similarity }=\frac{\sum_{i=1}^{\text{n}}\text{A}_{\text{i}} \cdot\text{B}_{\text{i}}}{\sqrt{\sum_{i=1}^{\text{n}}\text{A}_{\text{i}}^{2} \cdot\sqrt{\sum_{i=1}^{\text{n}}\text{B}_{\text{i}}^{2}}}} \tag{4}\]  
where A\({}_{\text{i}}\) and B\({}_{\text{i}}\) are the observations of the signals of two plants (vectors A and B). The numerator \(\sum_{i=1}^{\text{n}}\text{A}_{\text{i}}\cdot\text{B}_{\text{i}}\) is the dot product of the two vectors. The denominator is the product of the norms of vectors A and B. This metric quantitatively demonstrated that the differences between the electrical signals were minimal, with an average cosine similarity value close to 1 (0.9969 for all 15 plants), reflecting a high degree of similarity among the signals. Based on this result, a single representative signal was selected for subsequent analyses. This approach ensures that the next stages of the study focus on detailed signal characterization without redundant  
Figure 1: The electrical signal of the _A. vera_ plant. computations, in addition to being a previously proposed approach to validate the similarity between signals [33]. Once the measurements of the electrical signals of the _A. vera_ plant were reproducible, the power spectrum was determined. The power spectrum represented in Figure 2 is characterized by a predominant concentration of energy in the lower frequencies. As the frequency increases, the power decays rapidly, following a behavior commonly described in the literature. This drop is particularly noticeable up to about 1 Hz. This type of spectrum is similar to that observed in the literature, where due to the very low frequencies, it appears to contain no energy; however, this is a result that indicates that further analysis and other techniques are required [18]. But it can be observed that the power spectrum shown does not adequately reflect the frequency variations in the signal. Then, the implementation of the STFT to obtain a new power spectrum was necessary. To obtain a better resolution of the power spectrum, the short-time Fourier transform (STFT) was implemented. Figure 3 shows the power spectrum obtained from the signal. Figure 3: The power spectrum of the electrical signal of _A. vera_ determined by the short-time Fourier transform (STFT). a) Main event. Figure 2: Power spectrum of _A. vera_ electric signal. The spectrum shows that most of the signal power is concentrated at low frequencies. However, components at higher frequencies are also observed. This observation led to the analysis and use of the wavelet transform to have a better resolution and compression of the frequency behavior over time. The main event is observed by sample 200 with an abrupt response of the electrical signal. The concentration of power at low frequencies indicates a low-frequency main component. This may be related to a slow and continuous physiological process in the plant, such as the transport of nutrients through the xylem or the maintenance of cell turgor under controlled conditions. The high frequency components and the abrupt change correspond to the electrical response of the plant to an external stimulus (environmental or physical) or to an internal chemical activity of the plant. An example of these rapid changes might be related to salicylic acid production or phytoalexin synthesis in response to injury or pathogen attack.