A Comparison of Papoulis and Chebyshev Filters in the Continuous Time Domain

The subject of this paper is the revisit of the Chebyshev (equiripple) and Papoulis (monotonic or staircase) low-pass filter in order to compare. It can be stated the fair comparison of Papoulis and Chebyshev filters cannot be found in the available literature. At the beginning, it is shown that ripple parameter may be used in order the Chebyshev filter to obtain a magnitude response having less passband ripple than the standard Chebyshev response. At the same time, the passband edge frequency is preserved at 3 dB. Further, the unified approach to design odd and even degree Papoulis filters is explained. For the purpose of comparison, the Chebyshev filter as a counterpart of the Papoulis filter is introduced. Thus obtained Chebyshev filter has the same stop band insertion loss, group delay and transient response as Papoulis filter. However, its passband performance is much better. It is shown that Chebyshev filter counterpart offers a better solution than Papoulis filter in all applications, except in ones applications where is required that passband attenuation to have a staircase shape.