Epilepsy is considered one of the primary neurological disorders, and its treatment requires abundant technological assistance. General Anaesthesia induces distinct patterns in brain activity, with the most common being a gradual increase in low-frequency signals as the level of Anaesthesia deepens. In this instance, a method of validating epileptic seizures and Anaesthesia through the utilization of electroencephalogram (EEG) data, acquired non-invasively, is introduced. Epileptic seizures and detection of the presence of Anaesthesia approaches make use of discrete Laplace Transformation (LT), Discrete Cosine Transformation (DCT), and Fast Fourier Transform (FFT). Here, it is discussed how power spectral analysis (PSA) helps study EEG characteristics in detecting epileptic behavior and the presence of Anaesthesia. A dataset of EEG (Epileptic and Anaesthesia), which is available publicly [1,2], has been used in the propounded technique using FIR filters and LT, DCT, and FFT are used to store and process 16 channel data. Power Spectrum Density (PSD) and its average were contrasted against a specific spectrum and frequency range of a typical EEG signal to obtain the results. This work uses a technique to determine whether the patient being studied is epileptic and awake or anesthetized.