The electromyogram (EMG) is an important tool for assessing the activity of a muscle and thus also a valuable measure for the diagnosis and control of respiratory support. In this article we propose convolutive blind source separation (BSS) as an effective tool to pre-process surface electromyogram (sEMG) data of the human respiratory muscles. Specifically, the problem of discriminating between inspiratory, expiratory and cardiac muscle activity is addressed, which currently poses a major obstacle for the clinical use of sEMG for adaptive ventilation control. It is shown that using the investigated broadband algorithm, a clear separation of these components can be achieved. The algorithm is based on a generic framework for BSS that utilizes multiple statistical signal characteristics. Apart from a four-channel FIR structure, there are no further restrictive assumptions on the demixing system.