A second-order digital filter section that implements two poles and two zeros in its transfer function, parameterized by five coefficients (b0, b1, b2, a1, a2) that determine its frequency response. It operates by computing y[n] = b0*x[n] + b1*x[n-1] + b2*x[n-2] - a1*y[n-1] - a2*y[n-2] on each input sample, using two delay elements to store prior samples and outputs. Its purpose is to serve as the fundamental building block for IIR filter implementation, where multiple biquad sections are cascaded to achieve higher-order responses, and it can realize low-pass, high-pass, band-pass, band-stop, peaking, and shelving filter types through coefficient selection. [formal: bi-quadratis | substrate: mind | horizon: a life | explicit: yes | epoch: 0.41]
Accepted ontology entry
biquad-filter
A second-order digital filter section that implements two poles and two zeros in its transfer function, parameterized by five coefficients (b0, b1, b2, a1, a2) that determine its frequency response. It operates by computing y[n] = b0*x[n]…
Definition
Why it is in scope
A human-made second-order filter section built to persist as the fundamental building block of IIR filter implementation in DSP systems, defined by its two poles and two zeros and parameterized by five coefficients per section.
Names and aliases
- biquad-filteren · CANONICAL
Relations from this entry
- cmspii7wx05i5jlssis320zjrDERIVED_FROM →
filter-design's accepted definition carves 'the structured practice of creating filters ... selecting an appropriate filter topology, computing coefficients or component values using synthesis methods (window method, bilinear transform, Chebyshev or elliptic approximation)'. Historically that practice — first analog (Butterworth/Chebyshev second-order prototypes), then digitized — is what produced the biquad: the bilinear transform maps a second-order analog prototype onto a second-order digital section, and realizing higher-order designs as cascaded second-order sections is a design-method choice for numerical stability. The practice existed first and fed into the biquad's form and its five-coefficient parameterization. This is historical origin (Law 7), not dependency: a biquad operates with no filter-design practice ongoing.
- iir-filterINSTANCE_OF →
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.
- audio-processingSERVES →
biquad-filter is a second-order IIR filter designed specifically to implement frequency-selective operations for audio signals; its purpose is to serve audio-processing tasks such as equalization and crossover filtering.
Relations to this entry
No accepted relations in this direction.
Record identity
- Created
- Sep 19, 2026, 5:50 AM UTC
- Content hash
- d5efba51bdbeffd0a68296603101a63187428a1f9cf524bdaf1ee58a0d46ba01