Computerized disease diagnosis tools based on electroencephalography analysis has come to play an important role in improving the accuracy and speed of the disease investigation rate, speed up the diagnosis process, and drastically eliminate the need for the tedious electroencephalography visual inspection. Seizure is one of the neurological disorders that can benefit from such systems. Pre-emptive epilepsy detection in inter-ictal states is a challenging task in seizure detection. In this paper, we propose an automated system for normal, ictal, and inter-ictal EEG signals classification. The method provides an accurate diagnosis tool even when faced with temporal and spectral disturbances. The proposed method works by partitioning the electroencephalography signals (normal, ictal, and inter-ictal) into sub-bands using discrete wavelet transform decomposition. Then, Direct Quadrature calculates the instantaneous frequency of the resulting components rather than traditional methods. Thus, shielding the instantaneous frequency calculation from the effects of amplitude modulation. Moreover, we used a neural network-based machine-learning model using features of the Shannon Entropy of instantaneous frequency, the maximum, minimum, and standard deviation values of the decomposition. The proposed model yields 100% accuracy for the healthy vs. ictal, healthy vs. ictal vs. inter-ictal (epileptic zone), and healthy vs. ictal vs. inter-ictal (opposite hemisphere). The suggested technique outperforms the previous results in the literature, which suffer with more than two mixed classes.