A filtering system for use in, for example, a radiological imaging in a mammography apparatus. The system has a roundabout carrying a set of filtration plates. Each filtration plate is held on the roundabout by a joint. In a parked or stationary position, each plate is vertically suspended and does not contribute to any unacceptable increase in the horizontal space requirement of an X-ray tube. Each filtration plate may be presented in turn before a window for the emission of X-rays from the tube. At this position, the plate is rectified about its joint in order to occupy one position, among several possible positions, that also makes it possible, in this way, to modulate the filtration capacity of the plate.