Design of optimum Nyquist signals based on generalized sampling theory for data communications

A new method is given for the optimal design of bandlimited Nyquist-type signal shapes for data communications, which maximizes its energy in a given time interval. The method is based on the periodically nonuniform sampling (PNS) theory making use of the linear splines. The computation is straightforward, and the constraint for intersymbol interference is shown to be easy to include in the problem. A numerical example is given, and performance of the optimal signal shapes is compared with that resulting from the use of previously obtained signal shapes in the literature. It is also concluded that the optimal signal shapes thus obtained are almost immune to small offsets at the sampling instants.