We propose systematic design methods for realization of a given LTI compensator with complex poles using a modulated-demodulated control framework. Applicability of the proposed realization methods is established through simulations performed on an undamped resonant plant compensated by a low gain controller to obtain better noise rejection performance. It is demonstrated how a modulated-demodulated structure may reduce the sampling rate in a hybrid control system. In addition, superior robust performance is achieved against variations in baseband parameters using direct reference injection into the modulated-demodulated control systems compared to the indirect injection approach. (C) 2014 Elsevier Ltd. All rights reserved.