Heart murmurs provide valuable information about mechanical activity of the heart, which aids in diagnosis of various heart valve diseases. This work does automatic and accurate heart murmur detection from phonocardiogram (PCG) recordings. Two public PCG datasets (CirCor Digiscope 2022 dataset and PCG 2016 dataset) from Physionet online database are utilized to train and test three custom neural networks (NN): a 1D convolutional neural network (CNN), a long short-term memory (LSTM) recurrent neural network (RNN), and a convolutional RNN (C-RNN). We first do pre-processing which includes the following key steps: denoising, segmentation, re-labeling of noise-only segments, data normalization, and time-frequency analysis of the PCG segments using wavelet scattering transform. We then conduct four experiments, first three (E1-E3) using PCG 2022 dataset, and fourth (E4) using PCG 2016 dataset. It turns out that our custom 1D-CNN outperforms other two NNs (LSTM-RNN and C-RNN). Further, our 1D-CNN model outperforms the related work in terms of accuracy, weighted accuracy, F1-score and AUROC, for experiment E3 (that utilizes the cleaned and re-labeled PCG 2022 dataset). As for experiment E1 (that utilizes the original PCG 2022 dataset), our model performs quite close to the related work in terms of weighted accuracy and F1-score.