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Sampling of discontinuous audio signals with rich spectra is a valuable asset in subtractive synthesis, but results in aliasing distortion. This letter proposes an aliasing-reduction technique, which is cost-effective, transient-free, and extensible to various discontinuities. It replaces the samples on a finite region around each discontinuity with values taken from a smooth polynomial, based on a novel interpretation of the differentiated polynomial waveform (DPW) method. In the musical pitch range, the number of operations in the proposed method is at least 40% smaller than in the DPW algorithm. The method is widely usable in sound synthesis applications.