Digital signal processing (DSP) is widely exploited in the modern world to enable a vast array of high performance services and devices that were unimaginable several years ago. As a highly pervasive technology, DSP considerably enhances everyday life by enabling applications ranging from anti lock breaking systems to satellite navigation and sophisticated medical imaging. DSP has also been an enabler for many of the highly successful communications technologies over the last20 years. It is only in recent years that advanced DSP has been utilized in optical communications to realize commercial long-haul optical systems in the form of DSP-enable coherent optical receivers, which not only offer high transmission capacities of the order of 100 Gb/s per wavelength, but achieve ultra sensitive receivers for radically increasing unrepeated transmission distances. Index Terms: Digital signal processing,OFDM,Passive optical networks.