Power electronic systems tend to be great contributors to faults in many applications especially wind turbines because they are exposed to harsh operation conditions in height. Thus, a great attention has been paid to fault diagnosis technologies. In this paper, the concept of an exact recovery under a sparse fault assumption is applied to the diagnosis of three-phase DC-AC power electronic inverter, this method is denoted as Sparse Recovery Diagnosis (SRD). This method has the advantage to reconstruct on-line a vector of numerous faults from a few system measurements and with finite-time convergence. In this paper, the concept of an exact recovery under a sparse fault assumption is applied to the diagnosis of three-phase DC-AC power electronic inverter, this method is denoted as Sparse Recovery Diagnosis (SRD). In order to apply the proposed method, it is first necessary to have a dynamical modeling without and with each considered fault. After that, roughly speaking, some assumptions (Sparsity, Restrictive Isometry Property) are necessary with respect to the influence of the fault on the measured signals, in order to apply an exact SRD method. The algorithm used in this paper is based on homogeneous observer. Moreover, in order to take into account the quality of the measured noisy signals, the homogeneity degree is variable. The paper ends by some simulation results on a case study which highlight the well founded of the proposed algorithm with respect to previous algorithms that did not consider that the measurement is noisy.