Estimations indicate that epilepsy is a disorder affecting over 50 million people worldwide, according to the World Health Organization (WHO). Electroencephalogram (EEG)-based seizure classification not only aids in diagnostics but also greatly contributes to epileptic management. However, the task of feature extraction and classification is the most challenging, specifically in detecting seizure periods (ictal) and non-seizure periods (interictal). This paper is devoted to exploring the effects of seizures on brain waves at different ranges of frequencies, including alpha, beta, delta, theta, and gamma. By applying a Finite Impulse Response (FIR) filter followed by an Independent Component Analysis (ICA) algorithm, we ensure that all the extracted features are independent, facilitating the classification of clinical disorders using Long Short-Term Memory (LSTM). The proposed diagnostic system yields promising results, with an average class accuracy interval ranging from 96.65% to 99.69% for the MIT dataset. Additionally, the mean squared error (MSE) value is recorded as 0.0057, indicating the superior performance of our model, while the signal-to-noise ratio (SNR) measures 18.78 dB, indicating a relatively strong signal-to-noise ratio. This research sheds light on the intricate dynamics of EEG signals during epileptic seizures, offering insights into the development of effective classification methodologies for improved epilepsy diagnosis and treatment. Notably, the features utilized in our study include EEG signals encompassing various frequency ranges, and our classification model aims to distinguish between seizure and non-seizure periods, comprising two output classes for effective seizure detection.