A digital communications transmitter (100) includes a digital linear-and-nonlinear predistortion section (200, 1800) to compensate for linear and nonlinear distortion introduced by transmitter-analog components (120). A direct-digital-downconversion section (300) generates a complex digital return-data stream (254) from the analog components (120) without introducing quadrature imbalance. A relatively low resolution exhibited by the return-data stream (254) is effectively increased through arithmetic processing. Distortion introduced by an analog-to-digital converter (304) may be compensated using a variety of adaptive techniques. Linear distortion is compensated using adaptive techniques with an equalizer (246) positioned in the forward-data stream (112). Nonlinear distortion is then compensated using adaptive techniques with a plurality of equalizers (226) that filter a plurality of orthogonal, higher-ordered-basis functions (214) generated from the forward-data stream (112). The filtered-basis functions are combined together and subtracted from the forward-data stream (112).