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Simple explicit expressions to estimate the Q-factor and the sensitivity of optically preamplified receivers with arbitrary optical filtering, which only require the eye-diagram analysis and the knowledge of the optical and electrical filters transfer functions, are proposed. The physical insight and fast computation time are its main advantages. The noise-equivalent bandwidths associated with the nonuniformity of the amplified spontaneous emission (ASE) noise spectrum at the photodetector input are fully characterized and taken into account in the expressions derivation. By using the noise-equivalent bandwidths, a simple way of designing the optical receiver filters to bound the impact of the ASE-ASE beat noise on the receiver performance is provided. Results show that this impact can be neglected for extinction ratio below 25 dB, as long as the optical-filter -3 dB bandwidth does not exceed 8× the bit rate. Numerical results reveal that our Q-factor expression provides acceptable estimates. Only for systems where the impact of the ASE-ASE beat noise is significant (high extinction ratio) or in case of low Q (below 4) and high intersymbol interference (ISI), less accurate estimates have been found. In case of high ISI and low Q, the accuracy is improved by taking the probability of occurrence of the nearest rails to the decision threshold in the eye-diagram into account.