Biquad filters are a two-pole two-zero IIR structure implementing most common EQ and filter types from six coefficients

A biquad (bi-quadratic) filter is the fundamental building block of digital EQ. It implements a second-order IIR (Infinite Impulse Response) filter using five active coefficients (b0, b1, b2 in the numerator; a1, a2 in the denominator; a0 is normalised to 1.0). Different combinations of these coefficients produce lowpass, highpass, bandpass, notch, allpass, high-shelf, low-shelf, and peaking EQ responses — virtually every EQ type used in audio production. Phase response depends on the filter type; allpass filters affect only phase. Cascading biquads produces higher-order filters. The biquad calculator tool lets engineers verify frequency and phase response before implementation.

Examples

A peaking EQ at 1 kHz, +6 dB, Q=1.0 requires calculating five coefficients from freq/samplerate, gain, and Q. The biquad can also be used as a comb filter: clearing b-coefficients and using a=[1,0,0,0,0,1] sums a signal with a 5-sample-delayed copy.

Assessment

Name the two output plots a biquad calculator should show when exploring an allpass filter, and explain why the amplitude plot alone is insufficient to characterise an allpass.