Ballistocardiography (BCG) signals play an important role in identifying hypertension. These signals coupled with machine learning methods can be used for detecting hypertension. In this study, we presented a novel feature engineering architecture to detect hypertension using BCG signals. In this work, we used a publicly available BCG signal dataset to develop the novel model. Our model consists of a unique feature extraction process, named the Odd-Even Pattern (OEP). This technique generates three specific feature vectors based on alternating odd and even indices when fed with BCG signals. We employed singular pooling to address the shortcomings of OEP in extracting advanced-level features. This technique combines singular value decomposition with statistical feature extraction to capture the intricate details from the BCG signals. We obtained 14 features by merging OEP with statistical features. We then employed two advanced feature selectors yielding 28 selected feature vectors, hence the model is named as OddEven28. The classification is done using k-nearest neighbors (kNN) algorithm, along with iterative majority voting. Our proposed OddEven28 model achieved a classification accuracy of 97.78% using six different feature vectors on the dataset. Our developed OddEven28 architecture performed better than the deep learning-based models developed for the automated detection of hypertension using BCG signals. The robustness of the model can be improved by training with huge diverse data obtained from various centers.