A nondifferentiable pulse with a more band-limited spectrum than a differentiable one

This letter contrasts two interpolating pulses with four sampling interval durations which interpolate cubic polynomials between successive samples. One yields an everywhere differentiable interpolant and the other an interpolant which is more band-limited despite not being everywhere differentiable. The continual need to interpolate intermediate values between data samples which arises in image processing makes it important to consider how interpolants differ from one another. This makes it of interest to compare two similar interpolating pulses which have the somewhat atypical behavior that the one with a continuous derivative is not the one with the more band-limited spectrum.