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In communication systems where full-duplex transmission is required, echo cancellers are deployed to cancel the interference of the transmitted signal at the collocated receiver. For systems using discrete multitone (DMT) modulation, echo cancellation is performed partially in the time and frequency domains to decrease the processing complexity. In this paper, echo cancellation for DMT systems is reformulated as a constrained optimization problem, where a cost function is minimized over an extended linear space. This extended space contains the weights of the finite-impulse-response (FIR) filter emulating the echo channel in the time and the frequency domains, while linear constraints are used to ensure the proper mapping between these two domains. Based on this proposed formulation, a new constrained adaptive echo cancellation structure for DMT-based digital subscriber lines (DSL) systems is proposed. The proposed formulation provides a unifying framework for different practical DSL systems (i.e., frame asynchronous and multirate), as well as additional flexibility in implementation by allowing the incorporation of supplementary constraints that can improve the performance of the system. As an illustrative example, we show how the robustness of the echo canceller can be improved in the presence of radio frequency interference by adding appropriate constraints on the extended linear space.