Bandpass digital differentiator design using quadratic programming

A novel technique utilizing quadratic programming for the design of bandpass FIR (finite impulse response) digital differentiators of arbitrary order is presented. The new differentiators have linear phase and are maximally accurate at the center of the differentiation band. Their design is based on a minimization procedure for the integrated square error of the frequency response over designated approximation bands. The closed-form solution for the filter coefficients is obtained by the method of Lagrange multipliers. The inclusion of stopband in the design process is also discussed. This technique has been successfully used by the authors for the design of optimal low pass differentiators. The new differentiators are important for applications where the first-, second-, or higher-order derivative of a digital signal is required to be accurate at midrange frequencies