sva_samples/measure/
bands.rs

1// Concern: one envelope per ERB band beside its impulse floor, or its knots within a dB bound | Non-concern: the discrete spectrum (spectrum.rs), what a band means | IO: (planes, rate, prune) -> bands
2
3use sva_formula::filter::Shape;
4
5use crate::biquad::{Coeffs, State, design};
6
7/// Glasberg and Moore's auditory filter width in Hz.
8pub fn erb_hz(hz: f64) -> f64 {
9    24.7 * (4.37 * hz / 1000.0 + 1.0)
10}
11
12/// One Cam is one filter width along the cochlea.
13pub fn cam(hz: f64) -> f64 {
14    21.4 * (1.0 + 4.37 * hz / 1000.0).log10()
15}
16
17pub fn hz_at_cam(cam: f64) -> f64 {
18    (10f64.powf(cam / 21.4) - 1.0) * 1000.0 / 4.37
19}
20
21/// 1 to 40 Cam is 26 Hz to 16.7 kHz.
22pub const FIRST_CAM: f64 = 1.0;
23pub const BAND_COUNT: usize = 40;
24
25/// Under the 2-3 ms gap-detection limit, a hundredth of the samples it came from.
26pub const DECIMATED_HZ: f64 = 2000.0;
27
28/// Sixteen time constants is past every band's peak.
29fn floor_secs(erb: f64) -> f64 {
30    (16.0 / erb).clamp(0.02, 2.0)
31}
32
33/// A filter cannot report an onset faster than its own, so a caller subtracts this.
34#[derive(Clone, Copy, Debug, PartialEq)]
35pub struct BandFloor {
36    pub peak: f64,
37    pub time_to_peak_secs: f64,
38    pub rise_10_90_secs: Option<f64>,
39}
40
41#[derive(Clone, Debug, PartialEq)]
42pub struct BandTrack {
43    pub centre_hz: f64,
44    pub cam: f64,
45    pub erb_hz: f64,
46    pub q: f64,
47    pub peak: f64,
48    pub time_to_peak_secs: Option<f64>,
49    pub rise_10_90_secs: Option<f64>,
50    pub floor: BandFloor,
51    pub rms: Vec<f64>,
52}
53
54#[derive(Clone, Debug, PartialEq)]
55pub struct Bands {
56    pub rate_hz: f64,
57    pub start_secs: f64,
58    pub bands: Vec<BandTrack>,
59}
60
61/// `hz: None` is the band's own ERB, capped at a quarter of the decimated rate.
62#[derive(Clone, Copy, Debug, PartialEq)]
63pub struct Smoothing {
64    pub hz: Option<f64>,
65    pub poles: usize,
66}
67
68const OWN_WIDTH: Smoothing = Smoothing { hz: None, poles: 1 };
69
70/// Squaring rectifies; the root at decimation makes the track an RMS.
71struct Chain {
72    pass: Coeffs,
73    smooth: Coeffs,
74    a: State,
75    b: State,
76    energy: Vec<State>,
77}
78
79impl Chain {
80    fn new(centre_hz: f64, sr: f64, smoothing: Smoothing) -> Chain {
81        let erb = erb_hz(centre_hz);
82        let hz = smoothing.hz.unwrap_or(erb.min(DECIMATED_HZ / 4.0));
83        Chain {
84            pass: design(Shape::Bandpass, centre_hz, centre_hz / erb, 0.0, sr),
85            smooth: design(Shape::OnePole, hz, 0.0, 0.0, sr),
86            a: State::default(),
87            b: State::default(),
88            energy: vec![State::default(); smoothing.poles],
89        }
90    }
91
92    #[inline]
93    fn step(&mut self, x: f64) -> f64 {
94        let banded = self.b.step(&self.pass, self.a.step(&self.pass, x));
95        self.energy
96            .iter_mut()
97            .fold(banded * banded, |e, pole| pole.step(&self.smooth, e))
98    }
99}
100
101fn trace(
102    centre_hz: f64,
103    sr: f64,
104    smoothing: Smoothing,
105    (hop, n, width): (usize, usize, usize),
106    at: impl Fn(usize, usize) -> f64,
107) -> Vec<f64> {
108    let mut chains: Vec<Chain> = (0..width)
109        .map(|_| Chain::new(centre_hz, sr, smoothing))
110        .collect();
111    let mut out = Vec::with_capacity(n / hop + 1);
112    for i in 0..n {
113        let mut each = chains
114            .iter_mut()
115            .enumerate()
116            .map(|(c, chain)| chain.step(at(c, i)));
117        let first = each.next().expect("a channel");
118        let energy = each.fold(first, |sum, e| sum + e) / width as f64;
119        if i % hop == 0 {
120            out.push(energy.max(0.0).sqrt());
121        }
122    }
123    out
124}
125
126/// Interpolated between the frames straddling it.
127fn crossing(track: &[f64], until: usize, level: f64, rate: f64) -> Option<f64> {
128    let hit = track[..=until].iter().position(|&v| v >= level)?;
129    if hit == 0 {
130        return Some(0.0);
131    }
132    let (lo, hi) = (track[hit - 1], track[hit]);
133    let frac = match hi > lo {
134        true => (level - lo) / (hi - lo),
135        false => 0.0,
136    };
137    Some((hit as f64 - 1.0 + frac) / rate)
138}
139
140fn stats(track: &[f64], rate: f64) -> (f64, Option<f64>, Option<f64>) {
141    let peak = track.iter().copied().fold(0.0, f64::max);
142    if peak <= 0.0 {
143        return (peak, None, None);
144    }
145    let at = track
146        .iter()
147        .position(|&v| v == peak)
148        .expect("the peak is one of the frames");
149    let t10 = crossing(track, at, 0.1 * peak, rate);
150    let t90 = crossing(track, at, 0.9 * peak, rate);
151    let rise = t10.zip(t90).map(|(a, b)| (b - a).max(0.0));
152    (peak, Some(at as f64 / rate), rise)
153}
154
155fn floor_of(centre_hz: f64, sr: f64, smoothing: Smoothing, hop: usize, rate: f64) -> BandFloor {
156    let n = (floor_secs(erb_hz(centre_hz)) * sr).round().max(4.0) as usize;
157    let track = trace(centre_hz, sr, smoothing, (hop, n, 1), |_, i| {
158        f64::from(u8::from(i == 0))
159    });
160    let (peak, at, rise) = stats(&track, rate);
161    BandFloor {
162        peak,
163        time_to_peak_secs: at.unwrap_or(0.0),
164        rise_10_90_secs: rise,
165    }
166}
167
168pub const HIGHEST_CENTRE_OF_RATE: f64 = 0.45;
169
170/// A centre the design cannot place is left out, never clamped onto the last it could.
171pub(crate) fn centres(sr: f64) -> Vec<f64> {
172    (0..BAND_COUNT)
173        .map(|k| hz_at_cam(FIRST_CAM + k as f64))
174        .filter(|hz| *hz < HIGHEST_CENTRE_OF_RATE * sr)
175        .collect()
176}
177
178pub fn least_rate_hz() -> f64 {
179    hz_at_cam(FIRST_CAM) / HIGHEST_CENTRE_OF_RATE
180}
181
182pub fn analyze(planes: &[&[f64]], sr: f64, start_secs: f64) -> Bands {
183    smoothed(planes, sr, start_secs, OWN_WIDTH)
184}
185
186pub const PRUNED_MODEL: &str = "each band's track as `bands` traces it, read at every source \
187                                sample instead of every 2 kHz one, in dB, 20 log10 of its \
188                                rms, any level under `floor_db` (the band's peak plus the \
189                                asked floor) cut to it. Its knots are a swing filter's \
190                                (Elmeleegy, H. et al. (2009), Online piece-wise linear \
191                                approximation of numerical streams with precision \
192                                guarantees, Proc. VLDB Endow. 2(1) 145-156): from each knot \
193                                the next is the last sample some line from it stays within \
194                                eps_db - g/2 of every sample since, its value that line's, \
195                                rounded to a grid of g dB, g the largest power of ten, at \
196                                most 1, not over eps_db / 5, so the polyline through the \
197                                stored knots is within eps_db of the cut track at every \
198                                source sample. `max_error_db` is the largest distance \
199                                between the two, evaluated there, the knots joined \
200                                linearly in dB. Peak, time to peak and rise are read off \
201                                every source sample, the impulse floor too";
202
203/// The fewest decimals a pruned knot is written to: the grid's step is at most a fifth of
204/// the bound.
205fn grid_per_db(eps_db: f64) -> f64 {
206    let decimals = (5.0 / eps_db).log10().ceil().max(0.0) as usize;
207    (0..decimals).fold(1.0, |per, _| per * 10.0)
208}
209
210/// Under this a bound is finer than the tens of dB a level spans hold in an f64, so no
211/// evaluated error could certify it: a correctness limit, not a cost one.
212pub const LEAST_PRUNE_DB: f64 = 1e-6;
213
214/// `eps_db` over `LEAST_PRUNE_DB`; `floor_db` under 0, against each band's own peak.
215#[derive(Clone, Copy, Debug, PartialEq)]
216pub struct Prune {
217    pub eps_db: f64,
218    pub floor_db: f64,
219}
220
221/// A source sample's index from the read's start, and the level there in dB.
222pub type Knot = (usize, f64);
223
224#[derive(Clone, Debug, PartialEq)]
225pub struct PrunedBand {
226    pub centre_hz: f64,
227    pub cam: f64,
228    pub erb_hz: f64,
229    pub q: f64,
230    pub peak: f64,
231    pub time_to_peak_secs: Option<f64>,
232    pub rise_10_90_secs: Option<f64>,
233    pub floor: BandFloor,
234    /// `None` where the band never sounds, and holds no knot.
235    pub floor_db: Option<f64>,
236    pub max_error_db: f64,
237    pub knots: Vec<Knot>,
238}
239
240/// `rate_hz` is the source rate a knot's index counts at.
241#[derive(Clone, Debug, PartialEq)]
242pub struct PrunedBands {
243    pub rate_hz: f64,
244    pub start_secs: f64,
245    pub prune: Prune,
246    pub bands: Vec<PrunedBand>,
247}
248
249pub fn pruned(planes: &[&[f64]], sr: f64, start_secs: f64, prune: Prune) -> PrunedBands {
250    let shape = (crate::measure::held(planes), planes.len());
251    PrunedBands {
252        rate_hz: sr,
253        start_secs,
254        prune,
255        bands: centres(sr)
256            .into_iter()
257            .map(|centre_hz| {
258                let (n, width) = shape;
259                let track = trace(centre_hz, sr, OWN_WIDTH, (1, n, width), |c, i| planes[c][i]);
260                let (peak, at, rise) = stats(&track, sr);
261                let floor_db = (peak > 0.0).then(|| 20.0 * peak.log10() + prune.floor_db);
262                let levels = |floor: f64| track.iter().map(move |v| (20.0 * v.log10()).max(floor));
263                let (knots, max_error_db) = match floor_db {
264                    Some(floor) => {
265                        let knots = swing(levels(floor), prune.eps_db);
266                        let worst = worst(levels(floor), &knots);
267                        (knots, worst)
268                    }
269                    None => (Vec::new(), 0.0),
270                };
271                let erb = erb_hz(centre_hz);
272                PrunedBand {
273                    centre_hz,
274                    cam: cam(centre_hz),
275                    erb_hz: erb,
276                    q: centre_hz / erb,
277                    peak,
278                    time_to_peak_secs: at,
279                    rise_10_90_secs: rise,
280                    floor: floor_of(centre_hz, sr, OWN_WIDTH, 1, sr),
281                    floor_db,
282                    max_error_db,
283                    knots,
284                }
285            })
286            .collect(),
287    }
288}
289
290/// As `PRUNED_MODEL` states. Each closed run's line holds every sample within `within`, and
291/// rounding its end to the grid moves it by at most half a step anywhere along the run.
292fn swing(levels: impl Iterator<Item = f64>, eps_db: f64) -> Vec<Knot> {
293    let per = grid_per_db(eps_db);
294    let on_grid = |db: f64| (db * per).round() / per;
295    let within = (eps_db - 0.5 / per) * (1.0 - 1e-9);
296    let mut levels = levels.enumerate();
297    let Some((_, first)) = levels.next() else {
298        return Vec::new();
299    };
300    let mut anchor = (0, on_grid(first));
301    let mut knots = vec![anchor];
302    let (mut last, mut lo, mut hi) = ((0, first), f64::NEG_INFINITY, f64::INFINITY);
303    let close = |anchor: Knot, (at, db): Knot, lo: f64, hi: f64| {
304        let run = (at - anchor.0) as f64;
305        let slope = ((db - anchor.1) / run).clamp(lo, hi);
306        (at, on_grid(anchor.1 + slope * run))
307    };
308    for (at, db) in levels {
309        let run = (at - anchor.0) as f64;
310        let (low, high) = (
311            (db - within - anchor.1) / run,
312            (db + within - anchor.1) / run,
313        );
314        if low.max(lo) > high.min(hi) {
315            anchor = close(anchor, last, lo, hi);
316            knots.push(anchor);
317            let run = (at - anchor.0) as f64;
318            (lo, hi) = (
319                (db - within - anchor.1) / run,
320                (db + within - anchor.1) / run,
321            );
322        } else {
323            (lo, hi) = (low.max(lo), high.min(hi));
324        }
325        last = (at, db);
326    }
327    if last.0 > anchor.0 {
328        knots.push(close(anchor, last, lo, hi));
329    }
330    knots
331}
332
333/// The polyline through `knots`, linear in dB, against every level it stands for.
334fn worst(levels: impl Iterator<Item = f64>, knots: &[Knot]) -> f64 {
335    let mut joins = knots.windows(2).peekable();
336    let mut most = 0f64;
337    for (at, db) in levels.enumerate() {
338        let line = match joins.peek() {
339            None => knots[0].1,
340            Some(&[a, b]) => a.1 + (b.1 - a.1) * (at - a.0) as f64 / (b.0 - a.0) as f64,
341            Some(_) => unreachable!("windows of two"),
342        };
343        most = most.max((line - db).abs());
344        if joins.peek().is_some_and(|pair| at == pair[1].0) {
345            joins.next();
346        }
347    }
348    most
349}
350
351pub fn smoothed(planes: &[&[f64]], sr: f64, start_secs: f64, smoothing: Smoothing) -> Bands {
352    let shape = (crate::measure::held(planes), planes.len());
353    let hop = (sr / DECIMATED_HZ).round().max(1.0) as usize;
354    let rate = sr / hop as f64;
355    Bands {
356        rate_hz: rate,
357        start_secs,
358        bands: centres(sr)
359            .into_iter()
360            .map(|centre_hz| {
361                let (n, width) = shape;
362                let track = trace(centre_hz, sr, smoothing, (hop, n, width), |c, i| {
363                    planes[c][i]
364                });
365                let (peak, at, rise) = stats(&track, rate);
366                let erb = erb_hz(centre_hz);
367                BandTrack {
368                    centre_hz,
369                    cam: cam(centre_hz),
370                    erb_hz: erb,
371                    q: centre_hz / erb,
372                    peak,
373                    time_to_peak_secs: at,
374                    rise_10_90_secs: rise,
375                    floor: floor_of(centre_hz, sr, smoothing, hop, rate),
376                    rms: track,
377                }
378            })
379            .collect(),
380    }
381}
sva_samples/measure/bands.rs

sva_samples/measure/
bands.rs
