Design of frequency-selective digital differentiators without frequency sampling and iterative optimization

We introduce the design scheme of frequency-selective digital differentiators which is the hybrid class between frequency-selective filter (band-pass filter) and differentiator. The response of the frequency-selective digital differentiators is more flexible than that of frequency-selective Alter or full-band differentiators. Hence, the frequency-selective digital differentiators are often more beneficiated than full-band differentiators in some applications. The features of the proposed method are as follows. First, the design problem can be formulated in the quadratic form without any frequency sampling. Second, thanks to the quadratic form, the solution is unique and the optimization scheme does not require any iterative optimization in order to get the solution. Accordingly, the procedure of the design of the frequency-selective differentiators is very simple. Also, the frequency-selective differentiators obtained by the proposed method have a robust stability since the maximum pole radius can be prescribed. To demonstrate the effectiveness of the proposed method, we show the numerical examples in the cases of low-pass differentiator and high-pass differentiator.