Comparison of the Continuous and Transient Performance of Five Classical Filter Designs for Impulsive Noise Characterization

This paper compares the continuous and transient performance of the five classical filter types (Bessel, Butterworth, Chebyshev, Chebyshev-Inverse, and Elliptic) using pure tones, a unit step response, and a synthetic impulsive waveform. The synthetic waveform has five components using six known distributions. All components are summed with a normal distributions (white noise). The distributions of the five components are arcsine, uniform, triangular, bernoulli, and beta distributions. The distributions are modelling noise sources (pure tone, sonic boom, noise with known peak compressions and rarefactions, synthetic maximal length sequence noise, and shaped sonic booms respectively). A qualitative comparison of the kurtosis statistic across the one-third-octave-bands from 125 Hz to 20 kHz shows that the flat roll off of the Bessel filters in the transition band causes a large reduction in the kurtosis levels of the adjacent bands. The other four filter designs have steeper transition band roll offs and did not have large reductions in the kurtosis near the adjacent frequencies. The Butterworth filters have the best combination of properties for characterizing continuous and transient waveforms.