ADHD is a neurodevelopmental disorder largely diffused among children and adolescents. The current method of diagnosis is based on agreed clinical literature such as DSM-5, by identifying and evaluating signs of hyperactivity and inattention. Multiple reviews have assessed that EEG is not sufficiently reliable for the diagnosis of ADHD. Theta-Beta Ratio is now the sole EEG parameter considered for analysis, although it is not robust enough to be utilized as a confirmatory technique for diagnosis. In this setting, new objective approaches for reliably classifying neurotypical and ADHD subjects are required. As a result, we suggest a new methodology based on Functional Data Analysis, a statistical class of methods for dealing with curves and functions. The initial stage in our method is to separate frequency bands from the EEG signal using a wavelet decomposition. We next compute the Power Spectral Densities of each of these bands and represent them as mathematical functions via spline interpolation. Finally, the relevance of the collected features is assessed using the Permutation ANOVA test. Using this method, we can detect different patterns in the PSDs of the groups and identify statistically significant features, confirming prior findings in the literature. We validate the features using classification techniques such as Bagging trees, Random Forest, and AdaBoost. The latter reaches the highest accuracy score of 76.65%, confirming the relevance of the extracted features.