Effective detection and classification of systolic and diastolic profiles in Phonocardiogram (PCG) are challenging not only due to the presence of other cardiac events but also due to the presence of non-cardiac events such as lung sounds, and speech. Due to the proximity of lungs and epiglottis with heart, the interference of lung sounds, and speech are unavoidable while recording PCG (from the subjects who suffer from respiratory dysfunction, cough, mental illness, etc.) using electronic stethoscope. This work presents a method for automatic classification of systolic and diastolic profiles of PCG corrupted with several noise components. The method involves constructing a unique dictionary matrix that captures the morphology of PCG signal and the noises which affects the fundamental heart sounds. The PCG signal is then decomposed over the dictionary matrix using sparse signal decomposition (SSD). The low frequency clean PCG signal with enhanced S1 and S2 sounds is then reconstructed by eliminating frequency components corresponding to various noises. Finally, by computing the Shannon entropy envelope followed by simple thresholding, S1 and S2 sounds are segmented. Time duration features obtained from segmentation are used for the classification of systolic and diastolic profiles. For the automated classification, hidden semi Markov model (HSMM), multilayer perceptron (MLP), support vector machine (SVM), and k nearest neighbor (KNN) classifiers are utilized and compared the performance metrics of the classifiers. To validate the proposed method, both real-time recorded PCG signals and signals taken from standard databases are considered. The proposed SSD based heart sound segmentation achieves an average accuracy of 99.55% for clean PCG, 99.23% for PCG corrupted with baseline wander (BW) and additive white Gaussian noise (AWGN), 99.44% for standard database, 99.18% for PCG corrupted with lung sounds, and 98.47% for PCG corrupted with speech. HSMM classifier results better classification F-measure over MLP, SVM, and KNN. The average F-measure of HSMM classifier for systolic and diastolic profiles classification of PCG is 96.74%.