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The problem of designing a transmit pulse such that after transmission over a dispersive channel the received pulse fits in a prescribed template can be formulated as a quadratic programming problem with affine semi-infinite constraints. In constrained optimisation, the optimal solution invariably lies on the boundary of the feasible set, and consequently perturbations on the optimal solution or the constraints means that the received pulses may no longer fit in the template. Perturbations to the optimal transmit pulse and the constraints arise, in practice, from errors in the implementation and uncertainty in the channel parameter, respectively. A robust formulation is presented which ensures that the constraints are satisfied even in the presence of implementation errors and channel parameter uncertainty. The technique developed is applied to determine the optimal transmit pulse shape to be programmed on a commercial T1 (1.544 Mbit/s) line interface unit.