bass-foundry/plugins/common/dsp/tests/blocks.rs

use common_dsp::meter::HarmonicMeter;
use common_dsp::oversample::Oversampler;
use common_dsp::svf::{Svf, SvfCoef};
use common_dsp::tracker::{NoteEvent, Tracker, TrackerConfig};
use common_dsp::{hz_to_midi, Saw};
use std::f32::consts::TAU;

const RATE: f32 = 48000.;

/// Steady-state gain in dB of a sine at `hz` through `f`.
fn sine_gain(mut f: impl FnMut(f32) -> f32, hz: f32) -> f32 {
    let n = (RATE * 0.5) as usize;
    let (mut pin, mut pout) = (0., 0.);
    for i in 0..n {
        let x = (TAU * hz * i as f32 / RATE).sin();
        let y = f(x);
        if i > n / 2 {
            pin += x * x;
            pout += y * y;
        }
    }
    10. * (pout / pin).log10()
}

#[test]
fn svf_bell_hits_its_gain_and_leaves_the_rest() {
    for (hz, db) in [(130., -12.), (400., 6.), (2000., -24.)] {
        let c = SvfCoef::bell(RATE, hz, 4., db);
        let mut s = Svf::default();
        let g = sine_gain(|x| s.process(&c, x), hz);
        assert!((g - db).abs() < 0.1, "{hz}: {g}");
        let mut s = Svf::default();
        let g = sine_gain(|x| s.process(&c, x), hz * 4.);
        assert!(g.abs() < 0.3, "{hz} away: {g}");
    }
}

#[test]
fn svf_bell_at_zero_db_is_an_exact_identity() {
    let c = SvfCoef::bell(RATE, 100., 2., 0.);
    let mut s = Svf::default();
    let mut saw = Saw::new(RATE, 55.);
    for _ in 0..4800 {
        let x = saw.sample();
        assert_eq!(s.process(&c, x), x);
    }
}

#[test]
fn svf_survives_retuning_every_sample() {
    let mut s = Svf::default();
    let mut saw = Saw::new(RATE, 55.);
    let mut peak: f32 = 0.;
    for i in 0..48000 {
        let hz = 40. + 4000. * (0.5 + 0.5 * (i as f32 * 0.003).sin());
        let c = SvfCoef::bell(RATE, hz, 8., 12.);
        let y = s.process(&c, saw.sample());
        assert!(y.is_finite());
        peak = peak.max(y.abs());
    }
    assert!(peak < 8., "{peak}");
    let c = SvfCoef::lowpass(RATE, 200., 0.707);
    let mut s = Svf::default();
    assert!(sine_gain(|x| s.process(&c, x), 2000.) < -35.);
    let c = SvfCoef::highpass(RATE, 200., 0.707);
    let mut s = Svf::default();
    assert!(sine_gain(|x| s.process(&c, x), 20.) < -35.);
}

#[test]
fn oversampler_round_trip_is_a_whole_sample_delay() {
    let mut o = Oversampler::new();
    let l = Oversampler::latency();
    let mut saw = Saw::new(RATE, 97.);
    let x: Vec<f32> = (0..9600).map(|_| saw.sample() * 0.5).collect();
    let y: Vec<f32> = x
        .iter()
        .map(|&v| {
            let u = o.up(v);
            o.down(u)
        })
        .collect();
    // Band-limited content passes; compare after the delay, away from the start.
    let mut err: f32 = 0.;
    let mut sig: f32 = 0.;
    for i in 2000..9600 {
        let d = y[i] - x[i - l];
        err += d * d;
        sig += x[i - l] * x[i - l];
    }
    let null = 10. * (err / sig).log10();
    // The saw has energy above the passband edge, so the null is limited by that, not by timing.
    assert!(null < -40., "{null}");
}

#[test]
fn oversampler_passband_is_flat_and_images_are_removed() {
    for hz in [50., 1000., 10000., 18000.] {
        let mut o = Oversampler::new();
        let g = sine_gain(
            |x| {
                let u = o.up(x);
                o.down(u)
            },
            hz,
        );
        assert!(g.abs() < 0.1, "{hz}: {g}");
    }
    // An image of a 1 kHz tone at 4× would sit at 47 kHz; check the 4× signal there.
    let mut o = Oversampler::new();
    let n = 48000;
    let (mut a, mut b) = (0f64, 0f64);
    let w = TAU as f64 * 47000. / (4. * RATE as f64);
    for i in 0..n {
        let x = (TAU * 1000. * i as f32 / RATE).sin();
        for (k, v) in o.up(x).into_iter().enumerate() {
            let t = (4 * i + k) as f64;
            a += v as f64 * (w * t).cos();
            b += v as f64 * (w * t).sin();
        }
    }
    let image = 20.
        * ((a * a + b * b).sqrt() / (2. * n as f64))
            .max(1e-12)
            .log10();
    assert!(image < -85., "{image}");
}

#[test]
fn harmonic_meter_reads_saw_harmonics() {
    let hz = 55.;
    let mut m = HarmonicMeter::new(RATE, 85.);
    let mut saw = Saw::new(RATE, hz);
    let mut done = 0;
    for _ in 0..48000 {
        if m.push(saw.sample(), hz) {
            done += 1;
        }
    }
    assert!(done >= 5);
    // A saw's k-th harmonic has peak 2/(πk).
    for k in 1..=16 {
        let want = 20. * (2. / (std::f32::consts::PI * k as f32)).log10();
        let got = m.levels()[k - 1];
        assert!((got - want).abs() < 0.5, "harmonic {k}: {got} vs {want}");
    }
}

#[test]
fn tracker_reports_notes_at_output_time() {
    let mut t = Tracker::new(RATE, TrackerConfig::BASS);
    t.set(false, -42., false);
    let l = t.latency();
    assert!(l < (0.08 * RATE) as usize, "{l}");
    let onset = 4800;
    let mut events = vec![];
    let mut saw_a = Saw::new(RATE, 87.31);
    let mut saw_b = Saw::new(RATE, 220.);
    for i in 0..onset + 48000 {
        let x = if i < onset {
            0.
        } else if i < onset + 24000 {
            0.5 * saw_a.sample()
        } else {
            0.5 * saw_b.sample()
        };
        t.process(x, |e| events.push((i, e)));
    }
    let starts: Vec<_> = events
        .iter()
        .filter_map(|(i, e)| match e {
            NoteEvent::Start { pitch, .. } => Some((*i, *pitch)),
            _ => None,
        })
        .collect();
    assert_eq!(starts.len(), 2, "{starts:?}");
    assert!(
        (starts[0].0 as i64 - (onset + l) as i64).abs() <= 24,
        "{starts:?}"
    );
    assert!((starts[0].1 - hz_to_midi(87.31)).abs() < 0.2);
    assert!((starts[1].1 - hz_to_midi(220.)).abs() < 0.2);
}

#[test]
fn tracker_delays_midi_by_the_latency() {
    let mut t = Tracker::new(RATE, TrackerConfig::BASS);
    assert!(t.set(true, -42., true));
    let l = t.latency();
    let mut events = vec![];
    for i in 0..l + 2000 {
        if i == 100 {
            t.note_on(41);
        }
        if i == 600 {
            t.note_on(43);
        }
        if i == 900 {
            // Releasing the lower held note first leaves the top note; then the top ends it.
            t.note_off(41);
            t.note_off(43);
        }
        t.process(0., |e| events.push((i, e)));
    }
    assert_eq!(
        events,
        vec![
            (
                100 + l,
                NoteEvent::Start {
                    pitch: 41.,
                    glide: false
                }
            ),
            (
                600 + l,
                NoteEvent::Start {
                    pitch: 43.,
                    glide: true
                }
            ),
            (900 + l, NoteEvent::Stop),
        ]
    );
}