Here is an image comparing the Fourier transform (i.e., "frequency response") of several popular continuous-time IIR filters: Butterworth, Chebyshev, and elliptic filters. The filters in this illustration are all fifth-order low-pass filters.
As is clear from the image, elliptic filters are sharper than the others, but they show ripples in their passband.
There are several common kinds of linear filters:
* A low-pass filter passes low frequencies.
* A high-pass filter passes high frequencies.
* A band-pass filter passes a limited range of frequencies.
* A band-stop filter passes all frequencies except a limited range.
* An all-pass filter passes all frequencies, but alters the phase relationship among them.
* A notch filter is a specific type of band-stop filter that acts on a particularly narrow range of frequencies.
* Some filters are not designed to stop any frequencies, but instead to gently vary the amplitude response at different frequencies: filters used as pre-emphasis filters, equalizers, or tone controls are good examples of this
Band-stop and bandpass filters can be constructed by combining low-pass and high-pass filters. A popular form of 2 pole filter is the Sallen-Key type. This is able to provide low-pass, band-pass, and high pass versions. A particular bandform of filter can be obtained by transformation of a prototype filter of that class.
[edit] Mathematics of filter design
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