This paper presents a generalization of the Parity Space Method (PSM) for fault detection and isolation by means of pseudodifferential operators. It is shown that a number of recently suggested Parity Space approaches in continuous time can be treated within a generic framework. Disturbance rejection properties of the parity checks written as polynomials in a pseudodifferential operator are studied in terms of 2- and ∞-norms. A consequent analysis demonstrates superior performance of the sliding-window convolution operator-based PSM