In convex optimization techniques for optimal control design, the main challenge is to manage an infinite dimensional Youla parameter. To make the problem tractable, a finite basis has to be defined. While delay basis has been shown efficient for discrete LTI plants, common bases for continuous applications are generally inefficient and numerically bad conditioned. This paper presents a straightforward functional basis derived from piecewise linear approximation theory. Several associated results on LTI systems, related with convolution product and Laplace transformation, are developed.