Cognitive neuroscience investigates the intricate connections between brain function and mental processing to understand the cognitive architecture. Exploring the human brain, the epicenter of cognitive activity, offers valuable insights into underlying cognitive processes. To monitor brain states corresponding to various mental activities, appropriate measurement tools are essential. Electroencephalogram (EEG) signals serve as a valuable tool for recording patterns and changes in electrical brain activities. Leveraging non-linear signal processing techniques holds promise for advancing our understanding of brain activities during cognitive tasks. In this study, we analyze the electrical activity of the brain using EEG data collected from subjects engaged in a cognitive workload task. Employing wavelet-based analysis, we capture changes in the structure of EEG signals before and during a mental arithmetic task. Additionally, spectral analysis is conducted to discern alterations in the distribution of spectral contents of EEG signals. Our findings underscore the efficacy of wavelet-based analysis and spectral entropy in quantifying the time-varying and non-stationary nature of EEG recordings, offering effective frameworks for distinguishing between different cognitive activities. Consequently, these methods afford deeper insights into the cognitive architecture by tracking changes in the distribution of the time-varying spectrum.