Discrete Fourier transform computation using prime Ramanujan numbers (Q1370324)

The author gives an analytic upper bound on the degree of approximation \(A_N\) in the computation of the discrete Fourier transform if the length \(N\) is a prime Ramanujan number. That is, \(A_N\leq N^3(c_1-\widehat c_1)^2/3\sin{\pi\over 2N}\), where \(c_1= \cos{\pi\over 2N}\) and \(\widehat c_1\) is the approximation of \(c_1\).