Optimum Chebyshev low-pass filter with an arbitrary number of real-frequency transmission zero pairs

The paper examines the effect of introducing distinct pairs of finite transmission zeros into the characteristic function of an optimum Chebyshev all-pole filter. To ensure the equiripple stopband, the transmission zero locations are determined using the Newton–Raphson method. A novel approach is proposed to transform the characteristic function from its transcendental into a rational polynomial form. Notably, the derivation process is straightforward, eliminating the need for recursion or optimization. These filters preserve the same magnitude response in the passband, while achieving enhanced stopband performance compared to their equiripple all-pole counterparts. To illustrate the effectiveness of this method, an approximation procedure is presented for a 7th-degree optimum Chebyshev low-pass filter with one, two, or three distinct simple transmission zeros, achieving a minimum stopband attenuation of 50 dB. A comparative analysis demonstrates the enhanced performance of the proposed filters.