On design and applications of digital differentiators

Abstract

This paper deals with the design and applications of digital differentiators. For real time applications it is mandatory that a differentiator should have as small an order as possible. Different procedures available for the design of FIR and IIR type digital differentiators are presented. The IIR Type digital differentiators are obtained by inversion and magnitude stabilization of the existing digital integrators. In some applications like controls, waveshaping, oscillators and communications require a constant 90° phase for differentiators. In this paper an attempt is made to study about the variation of phase angle of digital differentiators with the application of fractional delay. The use of digital differentiators for the detection of edges in an image, QRS detection in an ECG signal is illustrated. It has been observed that the digital differentiators have shown superior performance compared to the well known gradient method. With the proven efficiency of the differentiators in various applications, they have been implemented in hardware using Verilog.