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Currents injected by CMOS digital circuit blocks into the power grid and into the substrate of a system-on-a-chip may affect reliability and performance of other sensitive circuit blocks. To verify the correct operation of the system, an upper bound for the spectrum of the noise current has to be provided with respect to all possible transitions of the circuit inputs. The number of input transitions is exponential in the number of circuit inputs. In this paper, we present a novel approach for the computation of the upper bound that avoids the untractable exhaustive exploration of the entire space. Its computational complexity is indeed linear in the number of gates. Our approach requires CMOS standard cell libraries to be characterized for injected noise current. In this paper, we also present an approach for this characterization of CMOS standard cells. Experimental results have proven the accuracy of both the algorithm and the noise current models used for the library characterization.