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.