Level crossings of a random trigonometric polynomial

Farahmand, Kambiz

doi:10.1090/S0002-9939-1991-1015677-4

Level crossings of a random trigonometric polynomial
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Proc. Amer. Math. Soc. 111 (1991), 551-557 Request permission

Abstract:

This paper provides an asymptotic estimate for the expected number of $K$-level crossings of the random trigonometric polynomial ${g_1}\cos x + {g_2}\cos 2x + \ldots + {g_n}\cos nx$, where ${g_j}(j = 1,2, \ldots ,n)$ are independent normally distributed random variables with mean $\mu$ and variance one. It is shown that the result for $K = \mu = 0$ remains valid for any finite constant $\mu$ and any $K$ such that $({K^2}/n) \to 0$ as $n \to \infty$.

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