Number of real roots of a random trigonometric polynomial. (1992)

• Record Type: Journal Article
• Authors: Farahmand, K.
• Is Part Of: Journal of applied mathematics and stochastic analysis. Volume 5:Number 4(1992)
• Page Start: 307
• Page End: 313
• Publication Date: 1992
• Subjects: number of real roots -- number of level crossings -- random trigonometric polynomial -- Kac- Rice formula; Mathematical models -- Periodicals; Computer simulation -- Periodicals; Computer science -- Mathematics -- Periodicals; Computer science -- Mathematics; Computer simulation; Mathematical models; Applied Mathematics; Periodicals; Electronic journals; 519.22
• DOI: 10.1155/S104895339200025X
• Languages: English
• ISSNs: 1048-9533

Abstract

Abstract : We study the expected number of real roots of the random equation g 1 cos θ + g 2 cos 2 θ + … + g n cos n θ = K where the coefficients g j 's are normally distributed, but not necessarily all identical. It is shown that although this expected number is independent of the means of g j, ( j = 1, 2, …, n ), it will depend on their variances. The previous works in this direction considered the identical distribution for the coefficients.