Obstructive sleep apnea (OSA) is a significant risk factor for hypertension, primarily due to intermittent hypoxia and sleep fragmentation. Predicting whether individuals with OSA will develop hypertension within five years remains a complex challenge. This study introduces a novel deep learning approach that integrates Discrete Cosine Transform (DCT)-based transfer learning to enhance prediction accuracy. We are the first to incorporate all polysomnography signals together for hypertension prediction, leveraging their collective information to improve model performance. Features were extracted from these signals and transformed into a 2D representation to utilize pre-trained 2D neural networks such as MobileNet, EfficientNet, and ResNet variants. To further improve feature learning, we introduced a DCT layer, which transforms input features into a frequency-based representation, preserving essential spectral information, decorrelating features, and enhancing robustness to noise. This frequency-domain approach, coupled with transfer learning, is especially beneficial for limited medical datasets, as it leverages rich representations from pre-trained networks to improve generalization. By strategically placing the DCT layer at deeper truncation depths within EfficientNet, our model achieved a best area under the curve (AUC) of 72.88%, demonstrating the effectiveness of frequency-domain feature extraction and transfer learning in predicting hypertension risk in OSA patients over a five-year period.