Extracting useful information from cardiac signals for the diagnosis of diseases and judgement of heart functioning is of special interest to medical personnel. However, exploiting such signals is subject to the availability of the signals themselves and to possible measurement errors. We thus argue that modelling such signals offers several advantages as compared to relying on measured data only. By using a formalized representation, the parameters of the signal model can be manipulated and/or modified, thus providing mechanisms that allow researchers to reproduce and control such signals by means of e.g. simulators. To guide both the signal modelling and simulator development phases, we propose a new generic framework. We then illustrate how it can be used to guide the modelling of the impedance cardiography and impedance respirography signals. We also show how the proposed framework has been used to guide the development of the corresponding Bio-Impedance Signal Simulator (BISS). As a result, the implemented BISS generates simulated Electrical Bio-Impedance (EBI) signals and gives freedom to the end-user to control the essential properties of the generated EBI signals depending on their needs. Predefined states of human conditions/activities are also included for ease of use.