The use of feature extraction and selection from EEG signals has shown to be useful in the detection of epileptic seizure segments. However, these traditional methods have more recently been surpassed by deep learning techniques, forgoing the need for complex feature engineering. This work aims to extend the conventional approach of epileptic seizure detection utilizing raw power spectra of EEG signals and convolutional neural networks (CNN). The proposed technique utilizes wavelet transform to compute the frequency characteristics of multi-channel EEG signals. The EEG signals are divided into 2 second epochs and frequency spectrum up to a cutoff frequency of 45 Hz is computed. This multi-channel raw spectral data forms the input to a one-dimensional CNN (1-D CNN). Spectral data from the current, previous, and next epochs is utilized for predicting the label of the current epoch. The performance of the technique is evaluated using a dataset of EEG signals from 24 cases. The proposed method achieves an accuracy of 97.25% in detecting epileptic seizure segments. This result shows that multi-channel EEG wavelet power spectra and 1-D CNN are useful in detecting epileptic seizures.