A Mixing of Prouhet-Thue-Morse Sequences and Rademacher Functions
Hieu D. Nguyen
TL;DR
This paper introduces a new generalization of the Prouhet-Thue-Morse sequence based on Rademacher functions, revealing orthogonality, recurrence relations, and applications in radar waveform sidelobe analysis.
Contribution
It presents a novel generalization of Prouhet-Thue-Morse sequences using Rademacher functions, with new orthogonality, recurrence properties, and radar applications.
Findings
Sequences satisfy orthogonality relations
Sequences exhibit specific recurrence relations
Application in describing radar waveform sidelobes
Abstract
A novel generalization of the Prouhet-Thue-Morse sequence to binary -weight sequences is presented. Derived from Rademacher functions, these weight sequences are shown to satisfy interesting orthogonality and recurrence relations. In addition, a result useful in describing these weight sequences as sidelobes of Doppler tolerant waveforms in radar is established.
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Taxonomy
TopicsMathematical Dynamics and Fractals · advanced mathematical theories · Quantum chaos and dynamical systems