Improving the time domain response of fractional order digital differentiators by windowing

In this paper, the limitation of using (jω)ν as the ideal frequency response of fractional order digital differentiators for non-bandlimited signals is discussed. High frequency error enhanced by (jω)ν, along with the cause of time domain response degradation, is presented. Windows are proposed, which can help to improve the time domain response of fractional order digital differentiator and greatly reduce the filter order if the differentiator is approximated by finite impulse response (FIR) filter. Simulation results show that windowing the output of fractional order digital differentiator in frequency domain is effective in improving the time domain response of signals.