bandpass

A biquad bandpass filter. Pass it a broadband signal (typically noise) and it carves out a resonant peak at center_hz, attenuating everything outside the band.

Signature

signal.bandpass(center_hz, q) -> Signal

• center_hz — the centre of the passband.
• q — the resonance / Q factor. Higher means a narrower peak. Roughly: bandwidth ≈ center_hz / q. Useful range 0.5 (very broad, about an octave wide) to 50 (very narrow, almost a sine).

The filter uses the constant-skirt-gain bandpass coefficients from the RBJ Audio EQ Cookbook — the standard biquad for this job in audio software.

Why this exists

The DSL’s source primitives — sine, chirp, noise — are either spectrally pure (sines, chirps) or perfectly flat (noise). Realistic sounds usually have shaped spectra that are neither: a hum tone at some specific frequency with side-lobes around it, or a broadband crackle that rolls off above a certain frequency. You get those shapes by filtering broadband content rather than by summing pure tones.

The classic example is a resonant body — a bell, a sonar transducer housing, a tube. Strike it with broadband energy (a hammer hit, an electrical impulse) and the body’s resonance carves the broadband spectrum into one or more peaks. We model that as noise(...).bandpass(...).

Example: a single-peak ping

patch("hum", "one_shot",
    noise("white", 1.0)
        .bandpass(1000.0, 12.0)        // 1 kHz peak, ~80 Hz wide
        .env(0.005, 1.2)
        .gain(0.5));

That’s a 1 kHz tonal hum with a noisy texture — the noise inside the passband shows up as “jagged” amplitude variation across the peak in an FFT, distinct from the pinpoint spike a pure sine would produce.

Example: subtractive ping with two peaks

patch("ping", "one_shot",
    mix([
        noise("white", 1.0).bandpass(1000.0, 12.0).gain(0.5),  // 1 kHz fundamental
        noise("white", 1.0).bandpass(2050.0, 12.0).gain(0.4),  // 2 kHz, octave up
        noise("white", 1.0).bandpass(3200.0, 1.5).gain(0.15),  // broad shoulder
    ]).env(0.008, 1.5).gain(0.45));

The first two filters create narrow resonances; the third uses a low Q to scoop out a broader high-frequency shoulder. This is the shape of many real metallic/transducer pings — broadband excitation through a multi-mode resonant body.

Notes

• Transient response. The biquad needs a few sample periods to settle from cold; the first ~5 ms of the output is a brief attack-like ramp. Usually masked by env(...) so it doesn’t matter.
• Very high Q can ring. At Q above ~50 the filter is essentially a resonator: it’ll continue ringing after the input ends. Sometimes this is what you want (struck-bell-like sustain); sometimes it’s an artefact. Drop Q if you don’t want it.
• Bandpass is a single tool. Combine multiple bandpass calls in parallel via mix(...) to build complex spectral shapes — that’s the workhorse pattern. Sequential bandpasses (one feeding another) don’t usually do what you want.
• Out-of-band content goes to roughly silence. The filter rolls off at 6 dB/octave per pole; the biquad gives you 12 dB/octave on each side of the peak. Below the centre by an octave, the level drops about 20 dB.