The Chebyshev type filter is named in honor of Pafnuty Chebyshev because their mathematical characteristics are derived from Chebyshev polynomials.
A PI filter is a filter that has a series element and two parallel elements connected in the shape of the Greek letter PI.
Chebyshev filters are analog or digital filters having a steeper roll-off and more passband ripple or stopband ripple than Butterworth filters. Chebyshev filters have the property that they minimize the error between the idealized filter characteristic and the actual over the range of the filter, but with ripples in the passband.
Chebyshev filters provide sharper rate of attenuation beyond the -3 db point. Chebyshev filters are more sensitive to component tolerances than Butterworth filters.
For even-order filters, all ripple is above the dc-normalized passband gain response, so cutoff is at 0 dB. For odd-order filters, all ripple is below the dc-normalized passband gain response, so cutoff is at -(ripple) dB.
A High pass filter is a filter that passes high frequencies, but attenuates frequencies lower than the cutoff frequency.