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A novel generalization of the Prouhet-Thue-Morse sequence to binary $\pm1$-weight sequences is presented. Derived from Rademacher functions, theseweight sequences are shown to satisfy interesting orthogonality and recurrencerelations. In addition, a result useful in describing these weight sequences assidelobes of Doppler tolerant waveforms in radar is established.

A Mixing of Prouhet-Thue-Morse Sequences and Rademacher Functions