Transform methods based designing of matrix fractional order differentiators

This paper presents the designs of matrix fractional order differentiator (MFOD) using transform based methods. Here, four transform methods are employed for MFOD design which includes discrete cosine transform (DCT), discrete sine transform (DST), discrete Fourier transform (DFT) and discrete Hartley transform (DHT) methods. The inefficiencies of conventional FIR and IIR MFOD design methods that arise due to causality and time-invariant limitations imposed on the MFOD are suitably eliminated using transform methods. The proposed MFODs are of closed-form and optimal in nature hence they perform better than conventional MFOD designs. The designed MFODs are applied to compute the fractional derivative of complex exponential sequence. To evaluate the performance of the proposed MFODs four design examples are presented with DCT, DST, DFT and DHT methods. Furthermore, the performance is measured in terms of average integral squared error and and variation of average integral squared error with discrete frequency points for different designs is observed. The results affirm that the proposed transform method of MFOD design is efficient and suitable for short data record filtering.