LAUSR

The orthogonal Jacobi polynomials are not suitable for the characteristic function in the continuous- and discrete-time filter designs because they are not fulfilling the basic conditions: to be pure odd or to be pure even. A simple modification of Jacobi polynomials, proposed in this Letter, is performed to obtain a new filter approximating function. Magnitude frequency responses of obtained filters exhibit more general behaviour compared to that of classical Gegenbauer (ultraspherical) filters, due to one additional parameter available in the Jacobi polynomials. This parameter can be used to obtain magnitude response with smaller passband ripple values (nearly monotonic behaviour), smaller group delay variations or sharper cutoff slope. The proposed modified Jacobi polynomials are not orthogonal; however, many known orthogonal polynomials can be obtained as theirs special cases.