Abstract
Systems of m equiangular lines spanning ℝd\documentclass[12pt]{minimal}
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$$\mathbb {R}^d$$
\end{document} or ℂd\documentclass[12pt]{minimal}
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$$\mathbb {C}^d$$
\end{document} that satisfy the so-called Welch bound have recently gained a lot of attention due to various applications in signal processing. Such sets are called equiangular tight frames (ETFs). One of the geometrically appealing aspects of an ETF is that any vector can be represented in terms of an ETF by using a dual frame that is also an equiangular set. However, for a given m and d, with m > d + 1, ETFs are rare. Here we study some properties of equiangular lines spanning ℝd\documentclass[12pt]{minimal}
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$$\mathbb {R}^d$$
\end{document} when the Welch bound is not met. Such equiangular sets are more common than ETFs. In this case, the properties of the canonical dual, in particular, the angle set of the canonical dual are studied. We determine conditions on equiangular lines spanning ℝd\documentclass[12pt]{minimal}
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$$\mathbb {R}^d$$
\end{document} whose canonical dual has few distinct angles.