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Pulse waveforms with overlapping yet orthogonal spectra are desired in high-rate multidimensional modulation and (carrier-free) orthogonal frequency division multiple access. To this end, we propose a digital filter solution to orthogonal pulse design for UWB impulse radios. A sequential design strategy is used in which the filter tap coefficients generating a new pulse are imposed with linear constraints to guarantee (spectral) orthogonality to all previously designed pulses. By formulating the overall pulse design problem as a set of convex subproblems, a sequence of orthogonal waveforms can be efficiently obtained using convex optimization methods. Complying with a prescribed (FCC) spectral mask, our orthogonal waveforms enjoy high power utilization efficiency compared with other orthogonal waveform alternatives.