Higher Order Low Pass FIR Digital Differentiators

Abstract

In this paper design of non-recursive higher order low pass digital differentiators satisfying given specifications is investigated. The concept of low pass differentiation is further generalized to higher order differentiators. A formula is derived using Fourier integral to compute impulse response coefficients of the differentiator. The equation is then used to design first order differentiators and results are compared with Salesnick's technique. The proposed FIR low pass differentiator has improvement in transition width and flexibility to choose cutoff frequency. The same technique has been demonstrated for second order design according to provided specifications. This method is used in the design of second order low pass differentiator for QRS detection in ECG. It is shown that the proposed implementation has low hardware and software complexity as compared to existing second derivative based techniques of QRS detection, giving advantage in optimization of current real time ECG systems.