The concurrent fault detection methods are generally based either explicitly or implicitly, on the use of redundancy. This paper presents a novel methodology for concurrent fault detection in linear digital systems. The basic principle of approach is the use of implicit analytical redundancy relations, i.e. relations between the measurement available variables. The robustness requirement of the redundancy relations guarantees a maximal sensitivity of the concurrent detector against fault and minimal sensitivity towards noise. Techniques for designing fault detection circuitry using optimal redundancy relations are discussed. Error detection capabilities of the scheme proposed in this work are efficient for a very large class of linear digital signal processor. The test circuit obtained for concurrent fault detector implementation is still very reasonable.