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Design of fractional order differentiator using discrete Hartley transform

In this paper, the design of fractional order differentiator is investigated. First, the discrete Hartley transform (DHT) interpolation method is described. Then, the non-integer delay sample estimation of discrete-time sequence is derived by using DHT interpolation. Next, the Grünwald-Letnikov derivative and non-integer delay sample estimation are applied to obtain the transfer function of fractional order differentiator. Finally, some numerical comparisons with conventional fractional order differentiators are made to demonstrate the effectiveness of this new design approach.