The modified Pascal polynomial approximation and filter design method
Hercules G. Dimopoulos, Elena Sarri · International Journal of Circuit Theory and Applications · 2010
SUMMARY Polynomial approximations are extensively used in analog and IIR digital filter design. In this paper, a comprehensive filter design and an optimization procedure are presented explicitly using a filter‐appropriate modified Pascal polynomial. The so‐designed all‐pole Pascal filters exhibit non‐equiripple passband and monotonic transition and stopband responses. The order of the new Pascal filters is calculated from the order inequality which, although it cannot be analytically solved, leads to a nomograph that has been created and is presented here. Inevitably, the mathematical complexity introduced by the nature of the Pascal polynomials makes the analytical expression of the poles of the transfer function unfeasible and for that reason poles are given by means of appropriate tables. The design method is demonstrated in several detailed examples and Pascal filters are compared with their all‐pole counterparts, Butterworth and Chebyshev, over which they reveal certain advantages and disadvantages. Copyright © 2010 John Wiley & Sons, Ltd.