Cardiovascular diseases (CVDs) are the leading global cause of death, which requires the early and accurate detection of cardiac abnormalities. Abnormal heart sounds, indicative of potential cardiac problems, pose a challenge due to their low-frequency nature. Utilizing digital signal processing and Phonocardiogram (PCG) analysis, this study employs advanced deep learning techniques for automated heart sound classification. Time- frequency representations capture multiple heart sound features, including gammatonegram, Mel-spectrogram, and Constant-Q Transform (CQT). A Convolutional Neural Network with Directed Acyclic Graph (DAG-CNN) architecture is designed and rigorously evaluated, achieving high classification accuracies of 100%, 99.7%, and 99.5% for gammatonegram, Mel-spectrogram, and CQT, respectively. Comparative analysis with pre-trained CNN models demonstrates the superior performance of the proposed model. This advancement in automated heart sound classification offers a promising and cost-effective tool for early diagnosis, particularly in resource-limited settings, helping to address the diagnostic gap and enhance cardiac care accessibility.