In this paper, channel equalization algorithms processing two samples of the received signal per channel symbol and operating in the frequency domain are described in a unifying framework. First, minimum mean-square error linear and decision-feedback equalizers are derived, and a synthesis technique based on the well-known Levinson-Durbin algorithm is proposed for the latter. Then, iterative linear and decision-feedback equalization algorithms for turbo processing are devised. Performance results for both uncoded and coded phase-shift keying transmissions show the efficacy of the proposed equalization techniques and their superiority over other existing frequency-domain equalization strategies.