A dispersion-compensating filter for next-generation low-cost analog and digital optical links is developed. In these high-frequency optical channels, even weak dispersion can be detrimental to data encoding (e.g., radar detection). Dispersion-compensating filters must be affordable for these low-cost channels, and they must be reliable for weak dispersion channels. In this paper, we design a dispersion-compensating filter based on three properties of the analog channel: weak modulation depth, a spectrally bounded signal, and a low-dispersion channel. We calculate the fundamental performance limits of the channel with and without the filter and quantify the improvement. Furthermore, numerical simulations are taken to estimate the filter's performances for both pulse amplitude modulation digital channels and for analog ones. The simulations agree with the analytical derivation, and, in both cases, the filter's integration improves the channels' performances considerably.