Design of Wideband Fractional-Order Differentiator Using Interlaced Sampling Method

[[abstract]]In this paper, the design of a wideband digital fractional-order differentiator (FOD) is investigated. First, conventional FOD designs are reviewed, and the reconstruction formula of the interlaced sampling method is used to design the proposed wideband FOD by index substitution and the Gr?nwald–Letnikov fractional derivative. Because a closed-form window design is obtained, the filter coefficients are easily computed. Then, the weighted least squares and convex optimization methods are applied to design non-sparse digital FODs that are optimal in the least squares or min–max sense. Next, the iterative hard thresholding and orthogonal matching pursuit methods are used to design sparse digital FODs to reduce the implementation complexity. Finally, several numerical examples are presented to show that the proposed FODs have smaller design errors in the high-frequency band than conventional digital FODs that do not use the auxiliary interlaced sampling signal