Chebyshev filter

<p>Chebyshev filters are <a href="/facts/Analog_filter/Vb9JRK8I">analog</a> or <a href="/facts/Digital_filter/2wcxCRdh">digital</a> filters that have a steeper <a href="/facts/Roll-off/CKNMMQ94">roll-off</a> than <a href="/facts/Butterworth_filter/3sQkLaqS">Butterworth filters</a>, and have either <a href="/facts/Passband/VebMrazm">passband</a> <a href="/facts/Ripple_(filters)/T9mzYBAh">ripple</a> (type I) or <a href="/facts/Stopband/rfIhELus">stopband</a> ripple (type II). Chebyshev filters have the property that they minimize the error between the idealized and the actual filter characteristic over the operating frequency range of the filter, but they achieve this with ripples in the frequency response. This type of filter is named after <a href="/facts/Pafnuty_Chebyshev/LzRqLqRm">Pafnuty Chebyshev</a> because its mathematical characteristics are derived from <a href="/facts/Chebyshev_polynomials/HoBINqgC">Chebyshev polynomials</a>. Type I Chebyshev filters are usually referred to as "Chebyshev filters", while type II filters are usually called "inverse Chebyshev filters". Because of the passband ripple inherent in Chebyshev filters, filters with a smoother response in the passband but a more irregular response in the stopband are preferred for certain applications.
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Chebyshev filter open-in-new

Chebyshev filter