iir-filter

iir-filter (infinite impulse response filter) is a specific type of digital filter that uses feedback. A competent speaker would call it 'a filter'. Nearest kind: filter. IIR filters have feedback coefficients in addition to feedforward.

iir-filter (infinite impulse response filter) operates within signal-processing as a constitutive domain. Remove signal-processing and the iir-filter concept ceases to operate — it needs the framework to function.

Pinned sense: the standard all-pass section is a specific kind of IIR filter. Its discrete-time form H(z) = (a + z^-1)/(1 + a z^-1) places a pole inside the unit circle with its zero at the reciprocal radius outside — precisely the feedback structure that gives IIR filters their infinite-duration impulse response; a nontrivial exact all-pass (unity magnitude for all frequency) cannot be realized as an FIR, only pure delays. A competent DSP speaker calls an all-pass section an IIR filter. Nearest kind on the board is iir-filter; 'filter' would leap two rungs up the ladder (Law 11e). Direction: specific all-pass -> general iir-filter, per Law 9.

Pinned sense (Law 11d): the classic Butterworth design as realized recursively — the maximally-flat prototype |H(jw)|=1/sqrt(1+(w/wc)^(2N)) carried to the digital domain by bilinear transform, with poles inside the unit circle and feedback in the difference equation. That realization is a specific member of the recursive filter class: a competent speaker calls a Butterworth IIR section an IIR filter. Nearest kind (Law 11e): iir-filter — no nearer recursive-kind rung exists in the web. FIR approximations of the Butterworth magnitude are a secondary sense, not the pinned one.

Biquad-filter is a second-order digital filter section with feedback (denominator coefficients a1, a2 in the difference equation). Under iir-filter's accepted definition — a recursive filter class characterized by the presence of feedback and an infinite-duration impulse response — a biquad is a specific kind of iir-filter. Nearest kind: iir-filter; the broader 'filter' kind is one rung further away through the accepted iir-filter INSTANCE_OF filter edge.