A Unified Framework of Digital Synthesis of Chebyshev and Elliptic Filter Using Frequency Domain and Bilinear Transform for 5G Applications

Abstract

Digital filtering in 5G front ends requires a design procedure that permits direct comparison of filter families under identical specifications. This study presents a unified comparative workflow for synthesising Chebyshev Type I and Elliptic digital filters using frequency-domain transformations followed by the bilinear transform. The filters were designed from matching low-pass prototypes with a sampling frequency of 40 GHz, a 12 GHz passband edge, a 15 GHz stopband edge, a maximum passband ripple of 0.1 dB, a minimum stopband-attenuation target of 60 dB, and a matched order of 14. Each prototype was transformed into High-Pass, Band-Pass, and Band-Stop configurations and then converted into the digital domain. Frequency response, phase response, group delay, impulse response, transition bandwidth, and stopband attenuation were evaluated using Python, SciPy, and Matplotlib. The digital Elliptic designs produced stopband attenuations of 72.8, 76.8, and 74.3 dB for the High-Pass, Band-Pass, and Band-Stop configurations, respectively, whereas the corresponding Chebyshev values were 58.3, 59.4, and 59.8 dB. The Elliptic filters also exhibited narrower transition regions, while the Chebyshev filters showed comparatively more favourable phase behaviour and simpler implementation characteristics. These results indicate that the two filter families provide complementary performance under the stated design conditions, supporting application-specific selection according to rejection, transition-band, phase, and delay requirements in 5G digital front ends.