Abstract: Improvements to amplitude phased keyed digital communications systems and to the processing of amplitude phase keyed symbols transmitted over radio frequency channels. The present invention provides for an amplitude phased keyed digital communications system including an adaptive baseband equalizer, a digital symbol recovery circuit in accordance with the present invention, and a quadrature demodulator. The adaptive baseband equalizer receives amplitude phased keyed signals and outputs in-phase and quadrature digital amplitude values corresponding to the received amplitude phased keyed signals. The digital symbol recovery circuit comprises a programmable addressable random access memory that stores a plurality of eight bit words comprising decoded symbol sets of the received amplitude phased keyed signals, and outputs the decoded symbol sets in response to addresses corresponding to the in-phase and quadrature output signals.