We present here a computational technique named Spline Harmonic Analysis in a new basis of the Spline—Vilenkin—Krestenson functions. The discrete Fourier transform in the basis of the Vilenkin—Krestenson functions is a special case of the new Spline Harmonic Analysis. We present more general spline functions. Cardinal splines and the Kotelnikov kernel are special cases of the new general spline functions. The new spline functions could be used in communication systems.