Polynomial Chebyshev Approximations of the Ideal Filter

Chebyshev error norms of polynomial approximations of the ideal filter complex transmittance are defined and procedures are developed to minimize these norms. The method emphasizes the role of the even and odd parts of the transfer function instead of the usual compromise between phase and amplitude. The resulting filter family is analyzed using an approximate analytical solution. Characteristics are compared with various classes of low-pass fliters.