Optimum design of finite duration nyquist signals

This paper presents a theoretical consideration of the optimal design of Nyquist type signals of M < ∞ baud time duration, which maximizes spectral energy inside a given bandqidth ω and which generates no intersymbol interference. The constraint for intersymbol interference is shown to be easily included into the problem. The optimum signal is a solution of a homogeneous linear equation with constraint. The computation is straightforward and involves the determination of eigenvectors of a symmetric matrix. Because of the fast converging nature of the prolate spheroidal wave functions used in the orthogonal expansion, the number of coefficients to determine the optimum signal is very small.