New algorithms for fast convolution based on convolution preserving spline signals

A discrete method for the convolution of odd-order splines is presented. The resulting algorithms are similar to those of fast convolution and contain the latter as a special case, as bandlimited functions may be interpreted as infinite-order splines. Finite-order spline interpolations offer besides their good approximation properties more flexibility, as discontinuities in the signals and their derivatives and strictly finite durations may be allowed for. In convolving a finite-duration signal with an infinite-duration one, overlap techniques can be used, which do not require more computation time and storage than conventional fast convolution algorithms.