Derivative approximations for sampled signals based on polynomial interpolation

We establish a new approach for approximating the continuous-time derivative of a signal from its discrete-time representation. This approach is based upon the polynomial-based generalized interpolation techniques and it can be efficiently implemented using the so-called Farrow structure. This method gives similar results as the derivative in the continuous time do main since the derivative is estimated with respect to a fractional interval. Interpolation filter design criteria leading to good derivative approximations are discussed. Design examples are given and they clearly illustrate that the interpolation filter design is quite critical. The well-known Lagrange interpolator designs do not provide good derivative approximations but the interpolation filter optimization techniques proposed earlier by the co-authors give much better results.