Summary: This paper introduces a new method for the design of robust fault reconstruction filters. The method is based on shaping the map from disturbance inputs to the fault estimation error through frequency weighting functions and formulating the problem as a robust observer design where the input-output error map is minimized by solving a set of matrix inequalities. The authors consider a numerical example consisting of ten states, two known inputs, four measured outputs, one disturbance, and three faults. Through this example, they show that the frequency shaping renders far superior performance than existing conventional methods when properly incorporated in the observer design problem.