We describe a machine learning approach to translate physiological signals from one representation to another, with application to the electrocardiogram. It is motivated by the fact that the modalities of signal acquisition by modern biomedical sensors may lead to non-standard representations. A novel neural network architecture is presented to address this issue, with a focus on the electrocardiogram (ECG). The model transforms the raw ECG measurements provided by an 11-channel contactless capacitive sensor mat into the standard 12-channel wet electrode ECG. To do this, a simplified version of the CycleGAN model, a bidirectional derivative of the generative adversarial network (GAN) architecture, is developed and evaluated with 32 parallel recordings of cardiac activity using the capacitive mat and a standard wet electrode set up. The mean quadratic error between the standard 12-lead ECG derivations and the corresponding translated mat signals by the proposed CycleGAN model shows the method\'s effectiveness.