Expression for denominator polynomial equation of chebyshev 1 filter
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Chebyshev filters are analog or digital filters having a steeper roll-off and more passband ripple (type I) or stopband ripple (type II) than Butterworth filters. Chebyshev filters have the property that they minimize the error between the idealized and the actual filter characteristic over the range of the filter (See references eg. [Daniels],[Lutovac]),[citation needed] but with ripples in the passband. This type of filter is named after Pafnuty Chebyshev because its mathematical characteristics are derived from Chebyshev polynomials. The type I Chebyshev filters are called usually as just "Chebyshev filters", the type II ones are usually called "inverse Chebyshev filters".
Because of the passband ripple inherent in Chebyshev filters, the ones that have a smoother response in the passband but a more irregular response in the stopband are preferred for some applications .[citation needed.