We have developed a minimally intrusive system to monitor respiratory movements of sleeping subjects. This system is based on a pressure transducer which measures the changes in air pressure inside an inflatable mattress on which the subject sleeps. Using a mechanical filter to protect the transducer against the large pressure changes due to sudden movements and subject weight, we can detect the more subtle movements of the subject's chest. This paper discusses the design of the monitoring system, including the design and modelling of the mechanical filter.