This paper presents an analytical method for designing FIR filters based on the hardware of time-delayed photonic neural networks for chromatic dispersion compensation in long-reach passive optical networks. The model employs a Fourier-based synthesis of the compensation function, allowing for the closed-form determination of phase and amplitude weights for each optical path. Different implementation strategies are considered, including solutions with phase-only control and others with additional amplitude control using tunable attenuators. Simulations over a 100 km standard single-mode fiber link demonstrate effective dispersion compensation for NRZ-OOK signals. In particular, the symmetric FIR-based design with 23 optical paths and 25 ps delay spacing achieved BER < 10-3 at data rates up to 40 Gbps under amplified spontaneous emission noise. These results confirm the analytical approach's potential to provide scalable, power-efficient, and high-speed solutions for future long-reach optical access networks.