Analysis and Design of Fractional Order Digital Differentiator

Abstract

Digital differentiator is an important signal processing tool. It is found in various applications like biomedical image enhancement and in high frequency radars. There are various techniques to design a digital differentiator and lot of modifications has done in this area to design several useful differentiators. But there is still scope of improvement in terms of parameter ‘optimization’. The design problem of differentiators is a challenging task.

Therefore, there is strong inspiration to make design process easy and efficient.

In this dissertation, the design of first and second order differentiator is studied. Next, the concept of higher order differentiator and fractional order differentiator is investigated. The study of Finite Impulse Response (FIR), digital differentiator is done and different orders of differentiator are compared with the ideal differentiator and calculated the error is calculated with different orders.

Secondly, a thorough study has been done on Fractional Order Savitzky Golay Digital Differentiator (FOSGDD). Here we have studied the method of design and then implemented this method for the calculation of derivative of a sinusoidal signal and chirp signal. The proposed method is compared with several popular methods and their root mean square error and computation time is computed. Also, the frequency response characteristic of the proposed method is studied by varying order and moving window coefficient .

A new method for the calculation of fractional order derivative using power function and least square method is also proposed. This method is imposed for the calculation of fractional order derivative and this method is compared with other popular method and its magnitude response and error characteristics are computed.