Methods and apparatus for directly detected optical system based on gapped CAP modulation and DSP Methods for generation and reconstruction of gapped CAP signal are disclosed. An apparatus for direct detection transmission for CAP modulated signal with two unbalanced optical sidebands separated by gaps is disclosed, in which a gapped CAP signal is generated, converted, and passed to an optical filter for unbalanced sidebands generation and wavelength locking before being transmitted over an optical link. Direct detection is performed on the optical signal and passed to gapped matching filters. Channel equalization is performed and the signal information is decoded to binary data.