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use signal::Signal;
use pitch::Pitch;
#[derive(Debug, Default, Clone)]
pub struct Correlation {
pub value: Vec<f32>
}
impl Correlation {
pub fn from_signal(signal: &Signal) -> Correlation {
let samples = &signal.samples;
Correlation {
value: (0..samples.len()).map(|offset| {
samples.iter().take(samples.len() - offset)
.zip(samples.iter().skip(offset))
.map(|(sig_i, sig_j)| sig_i * sig_j)
.sum()
}).collect()
}
}
pub fn find_fundamental_frequency(&self, signal: &Signal) -> Option<Pitch> {
if signal.is_silence() {
// silence
return None;
}
let first_peak_end = match self.value.iter().position(|&c| c < 0.0) {
Some(p) => p,
None => {
// musical signals will drop below 0 at some point
return None
}
};
let peak = self.value.iter()
.enumerate()
.skip(first_peak_end)
.fold((first_peak_end, 0.0), |(xi, xmag), (yi, &ymag)| if ymag > xmag { (yi, ymag) } else { (xi, xmag) });
let (peak_index, _) = peak;
let refined_peak_index = self.refine_fundamentals(peak_index as f32 - 0.5, peak_index as f32 + 0.5);
if self.is_noise(refined_peak_index) {
None
}
else {
Some(Pitch::new(signal.sample_rate / refined_peak_index))
}
}
fn refine_fundamentals(&self, low_bound: f32, high_bound: f32) -> f32 {
let data_points = 2 * self.value.len() / high_bound.ceil() as usize;
let range = high_bound - low_bound;
let midpoint = (low_bound + high_bound) / 2.0;
if (range * data_points as f32) < 1.0 {
midpoint
}
else {
let low_guess = self.score_guess(low_bound, data_points);
let high_guess = self.score_guess(high_bound, data_points);
if high_guess > low_guess {
self.refine_fundamentals(midpoint, high_bound)
}
else {
self.refine_fundamentals(low_bound, midpoint)
}
}
}
fn score_guess(&self, period: f32, data_points: usize) -> f32 {
(1..data_points).map(|i| {
let expected_sign = if i % 2 == 0 { 1.0 } else { -1.0 };
let x = i as f32 * period / 2.0;
let weight = 0.5 * i as f32;
expected_sign * weight * self.interpolate(x)
}).sum()
}
fn interpolate(&self, x: f32) -> f32 {
if x.floor() < 0.0 {
self.value[0]
}
else if x.ceil() >= self.value.len() as f32 {
self.value[self.value.len()-1]
}
else {
let x0 = x.floor();
let y0 = self.value[x0 as usize];
let x1 = x.ceil();
let y1 = self.value[x1 as usize];
if x0 as usize == x1 as usize {
y0
}
else {
(y0*(x1-x) + y1*(x-x0)) / (x1-x0)
}
}
}
fn is_noise(&self, fundamental: f32) -> bool {
let value_at_point = self.interpolate(fundamental);
let score_data_points = 2 * self.value.len() / fundamental.ceil() as usize;
let score = self.score_guess(fundamental, score_data_points);
value_at_point > 2.0*score
}
}
#[cfg(test)]
mod tests {
use super::*;
use std::f32::consts::PI;
const SAMPLE_RATE: f32 = 44100.0;
const FRAMES: u16 = 512;
fn frequency_resolution() -> f32 {
SAMPLE_RATE / 2.0 / f32::from(FRAMES)
}
fn sin_arg(f: f32, t: f32) -> f32 {
2.0 as f32 * PI * f * t
}
fn sample_sinusoid(amplitude: f32, frequency: f32) -> Signal {
let samples: Vec<f32> = (0..FRAMES)
.map(|x| {
let t = f32::from(x) / SAMPLE_RATE;
sin_arg(frequency, t).sin() * amplitude
}).collect();
Signal::new(&samples, SAMPLE_RATE)
}
#[test]
fn correlation_on_sine_wave() {
let frequency = 440.0f32; //concert A
let signal = sample_sinusoid(1.0, frequency);
let fundamental = Correlation::from_signal(&signal).find_fundamental_frequency(&signal).expect("Find fundamental returned None");
assert!((fundamental.hz-frequency).abs() < frequency_resolution(), "expected={}, actual={}", frequency, fundamental);
}
#[test]
fn interpolate_half_way() {
let corr = Correlation {
value: vec!(0.0, 1.0)
};
assert_eq!(0.5, corr.interpolate(0.5))
}
}
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