Studies on fractional order differentiators and integrators: A survey

Studies on analysis, design and applications of analog and digital differentiators and integrators of fractional order is the main objective of this paper. Time and frequency domain analysis, different ways of realization of fractance device is presented. Active and passive realization of fractance device of order 12 using continued fraction expansion is carried out. Later, time and frequency domain analysis of fractance based circuits is considered. The variations of rise time, peak time, settling time, time constant, percent overshoot with respect to fractional order αα is presented.Digital differentiators and integrators of fractional order can be obtained by using direct and indirect discretization techniques. The s to z   transforms used for this purpose are revisited. In this paper by using indirect discretization technique fractional order differentiators and integrators of order 12 and 14 are designed. These digital differentiators and integrators are implemented in real time using TMS320C6713 DSP processor and tested using National instruments education laboratory virtual instrumentation system (NIELVIS). The designed fractional order differentiators have been used for the detection of QRS sequences as well as the occurrence of Sino Atrial Rhythms in an ECG signal and also for the detection of edges in an image. The obtained results are in comparison with the conventional techniques.