A Design Method for Low-Delay Band-Pass Maximally Flat FIR Digital Differentiators with Stopband Based on Lp Norm Criterion

In this paper, we propose a design method of the low delay maximally flat band-pass FIR digital differentiators (DDs) with a stopband based on the L-p norm criterion. Conventional low-delay band-pass FIR DDs realize maximally fiat characteristics over the full range of the signal. However, the proposed DDs realize stopband based on the L-p norm criterion and low-delay simultaneously. Furthermore, the proposed DDs can also realize linear phase characteristics. In this paper, a design problem of the transfer function is substituted for a design problem of the inverse characteristics function. Therefore, it is easy to derive a function that satisfies the flatness conditions. The passband function of the inverse characteristics function is based on the L-p, norm criterion. However, we presented a straightforward method, in which minimized the L-p norm of the complex plane using Newton's method.