Abstract
Cardinal basis spline functions of second-order and third-order was clearly denoted, in order to encourage its recognition and new applications in the future. The basis function of infinite-order, which is known as the sampling function sinc(t), is used for the perfect reconstruction of the original signal from its periodically-sampled signal, based on the sampling theorem. By using the basis function of second-order or third-order as substitute for the sinc(t), we can reconstruct a continuous signal with frequently required smoothness of C1 or C2 continuity, under smaller amount of calculation. The reconstructed signals are also denoted in matrix forms of their polynomial equation, respectively.
