Spectrum of a Rudin–Shapiro-like sequence

We show that a recently proposed Rudin–Shapiro-like sequence, with balanced weights, has purely singular continuous diffraction spectrum, in contrast to the well-known Rudin–Shapiro sequence whose diffraction is absolutely continuous. This answers a question that had been raised about this new seque...

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Bibliographic Details
Published in:Advances in applied mathematics 2017-06, Vol.87, p.16-23
Main Authors: Chan, Lax, Grimm, Uwe
Format: Article
Language:English
Subjects:
Bartlett's algorithm
Spectral measure
Substitution dynamical system
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Summary:We show that a recently proposed Rudin–Shapiro-like sequence, with balanced weights, has purely singular continuous diffraction spectrum, in contrast to the well-known Rudin–Shapiro sequence whose diffraction is absolutely continuous. This answers a question that had been raised about this new sequence.
ISSN:0196-8858
1090-2074
DOI:10.1016/j.aam.2016.12.003