Noise sensitivity of band-limited signal derivative interpolation

The sensitivity of interpolation of the pth derivative of a band-limited signal directly from the signal's samples in the presence of additive stationary noise is considered. Oversampling and filtering generally decrease the interpolation noise level when the data noise is not band-limited. A lower bound on the interpolation noise level can be approached arbitrarily closely by increasing the sampling rate. The lower bound is equivalent to the noise level obtained by low-pass filtering and pth-order differentiation of the unsampled additive input noise.