kyma•tweaky . Learn . FilterTypeDefinition 
Contributions by: BenPhenix, DavidMcClain, CarlaScaletti, KurtHebel
Filters can be described by a number of different (somewhat orthogonal) characteristics:
Generally, when speaking of filters, we speak of the characteristics of a prototypical lowpass filter (for example, a Butterworth filter), transformed into the frequency response of interest (Butterworth bandpass filter). These filters are almost always IIR filters; however, it is possible to approximate these as FIR filters.
The same filter can be implemented in a variety of ways. Each implementation will have different performance characteristics (amount of noise, numbers of multiplies, mappings between parameters and coefficients).
Butterworth (Kyma IIR HP/LP filters): maximally flat amplitude response, no consideration of phase linearity or group delay variations. Filter has no amplitude ripple in the passband or stopband.
Linkwitz Riley, serial Butterworth filters: A 1pole Butterworth into 2nd 1pole Butterworth gives you a 2pole Linkwitz filter. 2 2pole Butterworths give you a 4pole Linkwitz, and so forth. Great for creating crossovers where keeping phase alignment is critical, common in speaker and audio components.
Here's an interactive tool for designing Butterworth filters.
Another interactive tool for Butterworth, Bessel and Chebyshev filters.
Bessel: retains nearly constant group delay through the passband with little consideration to amplitude response.
Chebyshev: produces passband, or stopband, ripples constrained within fixed bounds, such as 1 dB, 2 dB, and 3 dB of ripple. Ripples are either in the passband (Type I) or stopband (Type II). Subject to a high degree of nonlinear phase response.
Elliptic (Cauer filters): very sharp rolloff, very poor phase linearity, and have ripples both the passpand and stopband.
Finite Impulse Response Filter (Kyma FIR): FIR filters are stable, and have linear phase responses if the coefficients of the filter are symmetric about their center point (for example, 0.5, 1, 0.5). (In DSP circles, this kind of filter is defined as a class of digital filters that has only zeros on the zplane.)
The reason for the name is that if you feed an impulse (a single "1" followed by an infinite string of "0s") into an FIR, it eventually dies away. Its impulse response has a finite duration. An FIR is made up of delays and attenuators but no feedback. As anyone who's stuck a microphone in front of a speaker knows, feedback can "blow up" or grow without bounds (like a "pole" in an IIR filter). An FIR, not having feedback, can't blow up in the same way; hence its reputation for stability.
IIR filters require fewer multiplications and additions than FIR filters to achieve the same filtering action. (In DSP circles, this kind of filter is defined as a class of digital filters that has poles and zeros on the zplane.)
They are built of combinations of delays, attenuators, mixers, with feedback. They cannot have linear phase (or constant group delay), but with enough work an approximation to linear phase can be obtained.
AllPass (Kyma IIR Allpass): passes all frequencies with equal gain. Kyma filters have a nonlinear phase response see AllPass Discussion.
Reson: to quote DavidMcClain, "Reson filters have the desirable property of exhibiting constant peak amplitude across the entire frequency range, and the peak frequency can be directly specified. They have a postgain section to bring their outputs back up to where you want them." example no longer in the forum, perhaps David or someone can post the Reson filter example here.
Biquad, biquadratic: Dual path filter operating on the inphase and quadraturephase.
DavidMcClain 's microsound 2pole filters: discussion surrounding his DirectIIR filters
 Revision r1.9  27 Jan 2004  16:11 GMT  KurtHebel
