Objective: Fetal phonocardiography is a cost-effective and non-invasive method for monitoring of fetal health. However, the captured signal is often too noisy and unstable for reliable analysis. Detection of fetal heartbeats therefore requires a robust set of features to differentiate relevant sounds from background noise. We propose a novel set of features based on pitch shifting and psychoacoustics which lead to significant improvements of automatic fetal heartbeat detection. Methods: We collected, annotated, cleaned, processed and segmented microphone recordings taken from pregnant women. In addition, we employed a well-known simulated dataset to validate the methodology further. A total of 212 features were extracted, including classical audio features, psychoacoustic features, and features based on Empirical Mode Decomposition. Methods from statistical analysis and machine learning were applied to demonstrate the relevance of specific features. Afterwards, we trained a set of machine learning algorithms with different subsets of features. Results: Psychoacoustic features extracted from pitch-shifted signals are generally shown to be relevant and useful features for fetal heartbeat detection. When psychoacoustic features were added to the baseline features, classification accuracy of a robust classifier significantly increased from 69.24% to 76.16% for the real-world signals, and from 92.69% to 97.42% for one of the simulated datasets. Conclusion: The results demonstrate considerable gains in detection accuracy once pitch shifting and psychoacoustic modeling are applied to the input signal. Significance: Improvements achieved from applying psychoacoustics on fetal phonocardiographic signals might be an important finding in the effort of making remote monitoring of fetal wellbeing inexpensive and accessible.