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A novel method that allows the evaluation of the performance of an optically preamplified direct-detection baseband orthogonal frequency division multiplexing (OFDM) system with arbitrary optical and electrical filtering at the optical receiver is proposed. The method is based on the moment generating function of the symbol detected in each OFDM subcarrier after equalization and relies on the assumption that the noise samples at the fast Fourier transform (FFT) block input at the receiver side are practically uncorrelated. It is shown that, for typical filter bandwidths used in direct-detection optical OFDM systems (similar to or exceeding the OFDM signal bandwidth), the proposed method provides reasonably accurate estimates of the bit error probability for different electrical and optical filter types with various bandwidths, and for different numbers of OFDM subcarriers. For filter bandwidths smaller than the OFDM signal bandwidth, the proposed method becomes inaccurate due to the high correlation between the noise samples at the FFT block input.