In this article, we propose the optimization of the resolution of time-frequency atoms and the regularization of fitting models to obtain better representations of heart sound signals. This is done by evaluating the classification performance of deep learning (DL) networks in discriminating five heart valvular conditions based on a new class of time-frequency feature matrices derived from the fitting models. We inspect several combinations of resolution and regularization, and the optimal one is that provides the highest performance. To this end, a fitting model is obtained based on a heart sound signal and an overcomplete dictionary of Gabor atoms using elastic net regularization of linear models. We consider two different DL architectures, the first mainly consisting of a 1D convolutional neural network (CNN) layer and a long short-term memory (LSTM) layer, while the second is composed of 1D and 2D CNN layers followed by an LSTM layer. The networks are trained with two algorithms, namely stochastic gradient descent with momentum (SGDM) and adaptive moment (ADAM). Extensive experimentation has been conducted using a database containing heart sound signals of five heart valvular conditions. The best classification accuracy of $98.95\%$ is achieved with the second architecture when trained with ADAM and feature matrices derived from optimal models obtained with a Gabor dictionary consisting of atoms with high-time low-frequency resolution and imposing sparsity on the models.