A family of FIR differentiators based on a polynomial least squares estimation

To obtain the derivative of signals is necessary in several applications, from instrumentation to control or supervision. In some of them, only the first derivative is needed, but in other cases the second derivative could be also necessary. In this paper, a family of band-limited differentiators based on a polynomial least squares estimation of signals is presented. It is focused on obtaining a Finite-Duration Impulse Response (FIR) representation of such differentiators. The general formulas to calculate the FIR filter coefficients for the first and second derivatives are presented. Frequencial and temporal responses are compared with the ideal derivative responses. The benefits of using this approach in presence of noise and abrupt changes are shown in application examples.