Optical fiber communication systems have the advantages of long-distance transmission and large information capacity over traditional communication systems using copper cables. The signal processing can be performed in the electronic domain and/or the optical domain. As chromatic dispersion is one of the main transmission impairments, the aim of this research is to explore and develop optical signal processing for adaptive equalization, by replacing part of digital signal processing with optical signal processing. This thesis explores the self-calibration of a reconfigurable photonic integrated circuit (PIC) filter and the implementation of PIC as optical equalizers in an optical fiber communication system to compensate chromatic dispersion.