In the wake of Big Data, traditional Machine Learning techniques are now often integrated in the clinical workflow. Despite more capable, Deep Learning methods are not equally accepted given their unsatiated need for great amounts of training data and transversal use of the same architectures in fundamentally different areas with weakly-substantiated adaptations. To address the former, a cardiorespiratory signal synthesizer was designed by conditional sampling from a multimodally trained stochastic system of Gaussian copulas integrated in a Markov chain. With respect to the latter, a multi-branch convolutional neural network architecture was conceived to learn the best cardiac sensor-fusion strategy at every abstraction layer. The network was tailored to the tasks of cycle detection and classification for different cardiac modality combinations by a synthesizer-based data augmentation training framework and Bayesian hyperparameter optimization. The synthesizer yielded highly realistic signals in the time, frequency and phase domains for both healthy and pathological heart cycles as well as artifacts of different modalities. Benchmarking suggested that the network is able to surpass previous architectures and data augmentation provided a performance boost in realistic data availability scenarios. These included insufficient training data volume, as low as 150 cycles long, artifact contamination and absence of a classification data type in training.