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A new implementation of frequency domain online test approach is proposed for general digital linear time-invariant(LTI) systems. An analytical signal processing approach is used to extract the online test relation of LTI systems in frequency domain. An optimal implementation of the developed technique is proposed using sliding Goertzel DFT to reduce area and computational overheads with minimum error detection latency. Finite-precision analysis is done for fixed-point implementation of the proposed technique. The overhead is fixed and does not increase as complexity of LTI system increases. Simulation of fault detection capability is done for different filters using developed FLI fault injector platform.