Recently, a new set of biometric traits, called medical biometrics, have been explored for human identity verification. This study introduces a novel framework for recognizing human identity through heart sound signals, commonly referred to as phonocardiograms (PCGs). The framework is built on extracting and suitably processing Mel-Frequency Cepstral Coefficients (MFCCs) from PCGs and on a classifier based on a Multilayer Perceptron (MLP) network. A large dataset containing heart sounds acquired from 206 people has been used to perform the experiments. The classifier was tuned to obtain the same false positive and false negative misclassification rates (equal error rate: EER = FPR = FNR) on chunks of audio lasting 2 s. This target has been reached, splitting the dataset into 70% and 30% training and testing non-overlapped subsets, respectively. A recurrence filter has been applied to also improve the performance of the system in the presence of noisy recordings. After the application of the filter on chunks of audio signal lasting from 2 to 22 s, the performance of the system has been evaluated in terms of recall, specificity, precision, negative predictive value, accuracy, and F1-score. All the performance metrics are higher than 97.86% with the recurrence filter applied on a window lasting 22 s and in different noise conditions.