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Electronic signal processing is becoming very attractive to overcome various impairments that affect optical communications, and electronic dispersion compensation (EDC) represents a typical application in the currently designed systems. However, the inherent limits in performance achievable by electronically processing the signal at the output of a nonlinear photodetector have not received the attention they deserve. In this paper, we investigate the information-theoretic limits of electronic signal processing in transmission systems employing direct photodetection and two possible modulation formats: 1 on-off keying (OOK) with nonreturn-to-zero pulses; and 2 optical duobinary modulation (ODBM). The analysis is based on the computation of the information rate, i.e., the maximum achievable data transfer rate, and accounts for the modulation format as well as relevant parameters of the transmission scheme. In particular, we investigate the impact of sampling rate, uncompensated chromatic dispersion (CD), and quantization resolution of the electrical signal at the output of a direct photodetector. For OOK systems, the obtained results show that the optical signal-to-noise ratio penalty entailed by EDC can be limited to about 2 dB at most values of CD of interest in current applications. Moreover, ODBM systems at high values of CD can almost perform as OOK systems at zero CD. For all the considered modulation formats, the obtained results show that the received electrical signal can be sampled at a rate of two samples per bit interval and quantized with a precision of 3 bits per sample to practically achieve the ultimate performance limits.