Finite-Impulse-Response Digital Differentiators for Midband Frequencies Based on Maximal Linearity Constraints

Maximally linear digital differentiators (DDs) are known for high accuracy in narrow frequency bands centered at the frequency for which they are designed. In this paper, designs of DDs of odd and even lengths having maximal linearity at the middle of the frequency band are presented. Applying the maximal linearity constraints to the magnitude response of a differentiator gives a system of linear equations, which can be solved for the impulse response coefficients of the differentiator. It is observed that the coefficient matrices of these equations are Vandermonde matrices, and this helps in finding the solution of the equations in closed form. Design examples are presented to show the accuracy of the presented designs, and it is observed that even-length designs are more accurate in a significantly wider frequency band as compared with odd-length designs