A design of linear phase band-pass FIR digital differentiators with flat passband and Lp norm-based stopband characteristics

This paper describes a design of linear phase band-pass FIR digital differentiators with flat passband and L_p (1 ≤ p ≤ ∞) norm-based stopband characteristics. The transfer function consists of a passband function and a stopband function. The passband function guarantees the flat differential characteristics around an arbitrary center frequency. In addition, the maximally flat differentiators provide highly accurate differentiation around the desired frequency (the center frequency). The stopband function provides the L_p norm-based stopband while correcting the stopband region of the passband function. The coefficients of the stopband function are obtained through the quasi-minimization based on IRLS (Iterative Reweighted Least Squares) algorithm. The proposed design achieves the flexible stopband under the trade-off between the transition bandwidth and the size of side-lope ripple.