A variety of feature extraction and classification approaches have been proposed using electrocardiogram (ECG) and ECG-derived signals for improving the performance of detecting apnea events and diagnosing patients with obstructive sleep apnea (OSA). The purpose of this study is to further evaluate whether the reduction of lower frequency P and T waves can increase the accuracy of the detection of apnea events. This study proposed filter bank decomposition to decompose the ECG signal into 15 subband signals, and a one-dimensional (1D) convolutional neural network (CNN) model independently cooperating with each subband to extract and classify the features of the given subband signal. One-minute ECG signals obtained from the MIT PhysioNet Apnea-ECG database were used to train the CNN models and test the accuracy of detecting apnea events for different subbands. The results show that the use of the newly selected subject-independent datasets can avoid the overestimation of the accuracy of the apnea event detection and can test the difference in the accuracy of different subbands. The frequency band of 31.25–37.5 Hz can achieve 100% per-recording accuracy with 85.8% per-minute accuracy using the newly selected subject-independent datasets and is recommended as a promising subband of ECG signals that can cooperate with the proposed 1D CNN model for the diagnosis of OSA.