Transform a Digital Filter to Another Digital Filter Using Pascal’s Triangle

Two matrix equations, Pascal matrix equation and inverse Pascal matrix, are derived and demonstrated in this work. These matrix equations are used for making a conversion and inversion between the coefficients of an analog low pass filter transfer function H(s) and a digital transfer function H(z). The involving of the Pascal’s triangle in both matrix equations is helpful, easier to transform between analog filter and digital filter and therefore, the procedure of design a digital filter form another digital filter is presented in this paper.