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// BS1770 -- Loudness analysis library conforming to ITU-R BS.1770 // Copyright 2020 Ruud van Asseldonk // Licensed under the Apache License, Version 2.0 (the "License"); // you may not use this file except in compliance with the License. // A copy of the License has been included in the root of the repository. //! Loudness analysis conforming to [ITU-R BS.1770-4][bs17704]. //! //! This library offers the building blocks to perform BS.1770 loudness //! measurements, but you need to put the pieces together yourself. //! //! [bs17704]: https://www.itu.int/rec/R-REC-BS.1770-4-201510-I/en //! //! # Stereo integrated loudness example //! //! ``` //! # fn load_stereo_audio() -> [Vec<i16>; 2] { //! # [vec![0; 48_000], vec![0; 48_000]] //! # } //! # //! let sample_rate_hz = 44_100; //! let bits_per_sample = 16; //! let channel_samples: [Vec<i16>; 2] = load_stereo_audio(); //! //! // When converting integer samples to float, note that the maximum amplitude //! // is `1 << (bits_per_sample - 1)`, one bit is the sign bit. //! let normalizer = 1.0 / (1_u64 << (bits_per_sample - 1)) as f32; //! //! let channel_power: Vec<_> = channel_samples.iter().map(|samples| { //! let mut meter = bs1770::ChannelLoudnessMeter::new(sample_rate_hz); //! meter.push(samples.iter().map(|&s| s as f32 * normalizer)); //! meter.into_100ms_windows() //! }).collect(); //! //! let stereo_power = bs1770::reduce_stereo( //! channel_power[0].as_ref(), //! channel_power[1].as_ref(), //! ); //! //! let gated_power = bs1770::gated_mean(stereo_power.as_ref()); //! println!("Integrated loudness: {:.1} LUFS", gated_power.loudness_lkfs()); //! ``` use std::f32; /// Coefficients for a 2nd-degree infinite impulse response filter. /// /// Coefficient a0 is implicitly 1.0. #[derive(Clone)] struct Filter { a1: f32, a2: f32, b0: f32, b1: f32, b2: f32, // The past two input and output samples. x1: f32, x2: f32, y1: f32, y2: f32, } impl Filter { /// Stage 1 of th BS.1770-4 pre-filter. pub fn high_shelf(sample_rate_hz: f32) -> Filter { // Coefficients taken from https://github.com/csteinmetz1/pyloudnorm/blob/ // 6baa64d59b7794bc812e124438692e7fd2e65c0c/pyloudnorm/meter.py#L135-L136. let gain_db = 3.99984385397; let q = 0.7071752369554193; let center_hz = 1681.9744509555319; // Formula taken from https://github.com/csteinmetz1/pyloudnorm/blob/ // 6baa64d59b7794bc812e124438692e7fd2e65c0c/pyloudnorm/iirfilter.py#L134-L143. let k = (f32::consts::PI * center_hz / sample_rate_hz).tan(); let vh = 10.0_f32.powf(gain_db / 20.0); let vb = vh.powf(0.499666774155); let a0 = 1.0 + k / q + k * k; Filter { b0: (vh + vb * k / q + k * k) / a0, b1: 2.0 * (k * k - vh) / a0, b2: (vh - vb * k / q + k * k) / a0, a1: 2.0 * (k * k - 1.0) / a0, a2: (1.0 - k / q + k * k) / a0, x1: 0.0, x2: 0.0, y1: 0.0, y2: 0.0, } } /// Stage 2 of th BS.1770-4 pre-filter. pub fn high_pass(sample_rate_hz: f32) -> Filter { // Coefficients taken from https://github.com/csteinmetz1/pyloudnorm/blob/ // 6baa64d59b7794bc812e124438692e7fd2e65c0c/pyloudnorm/meter.py#L135-L136. let q = 0.5003270373253953; let center_hz = 38.13547087613982; // Formula taken from https://github.com/csteinmetz1/pyloudnorm/blob/ // 6baa64d59b7794bc812e124438692e7fd2e65c0c/pyloudnorm/iirfilter.py#L145-L151 let k = (f32::consts::PI * center_hz / sample_rate_hz).tan(); Filter { a1: 2.0 * (k * k - 1.0) / (1.0 + k / q + k * k), a2: (1.0 - k / q + k * k) / (1.0 + k / q + k * k), b0: 1.0, b1: -2.0, b2: 1.0, x1: 0.0, x2: 0.0, y1: 0.0, y2: 0.0, } } /// Feed the next input sample, get the next output sample. #[inline(always)] pub fn apply(&mut self, x0: f32) -> f32 { let y0 = 0.0 + self.b0 * x0 + self.b1 * self.x1 + self.b2 * self.x2 - self.a1 * self.y1 - self.a2 * self.y2; self.x2 = self.x1; self.x1 = x0; self.y2 = self.y1; self.y1 = y0; y0 } } /// Compensated sum, for summing many values of different orders of magnitude /// accurately. #[derive(Copy, Clone, PartialEq)] struct Sum { sum: f32, residue: f32, } impl Sum { #[inline(always)] fn zero() -> Sum { Sum { sum: 0.0, residue: 0.0 } } #[inline(always)] fn add(&mut self, x: f32) { let sum = self.sum + (self.residue + x); self.residue = (self.residue + x) - (sum - self.sum); self.sum = sum; } } /// The mean of the squares of the K-weighted samples in a window of time. /// /// K-weighted power is equivalent to K-weighted loudness, the only difference /// is one of scale: power is quadratic in sample amplitudes, whereas loudness /// units are logarithmic. `loudness_lkfs` and `from_lkfs` convert between power, /// and K-weighted Loudness Units relative to nominal Full Scale (LKFS). /// /// The term “LKFS” (Loudness Units, K-Weighted, relative to nominal Full Scale) /// is used in BS.1770-4 to emphasize K-weighting, but the term is otherwise /// interchangeable with the more widespread term “LUFS” (Loudness Units, /// relative to Full Scale). Loudness units are related to decibels in the /// following sense: boosting a signal that has a loudness of /// -<var>L<sub>K</sub></var> LUFS by <var>L<sub>K</sub></var> dB (by /// multiplying the amplitude by 10<sup><var>L<sub>K</sub></var>/20</sup>) will /// bring the loudness to 0 LUFS. /// /// K-weighting refers to a high-shelf and high-pass filter that model the /// effect that humans perceive a certain amount of power in low frequencies to /// be less loud than the same amount of power in higher frequencies. In this /// library the `Power` type is used exclusively to refer to power after applying K-weighting. /// /// The nominal “full scale” is the range [-1.0, 1.0]. Because the power is the /// mean square of the samples, if no input samples exceeded the full scale, the /// power will be in the range [0.0, 1.0]. However, the power delivered by /// multiple channels, which is a weighted sum over individual channel powers, /// can exceed this range, because the weighted sum is not normalized. #[derive(Copy, Clone, PartialEq, PartialOrd)] pub struct Power(pub f32); impl Power { /// Convert Loudness Units relative to Full Scale into a squared sample amplitude. /// /// This is the inverse of `loudness_lkfs`. pub fn from_lkfs(lkfs: f32) -> Power { // The inverse of the formula below. Power(10.0_f32.powf((lkfs + 0.691) * 0.1)) } /// Return the loudness of this window in Loudness Units, K-weighted, relative to Full Scale. /// /// This is the inverse of `from_lkfs`. pub fn loudness_lkfs(&self) -> f32 { // Equation 2 (p.5) of BS.1770-4. -0.691 + 10.0 * self.0.log10() } } /// A `T` value for non-overlapping windows of audio, 100ms in length. /// /// The `ChannelLoudnessMeter` applies K-weighting and then produces the power /// for non-overlapping windows of 100ms duration. /// /// These non-overlapping 100ms windows can later be combined into overlapping /// windows of 400ms, spaced 100ms apart, to compute instantaneous loudness or /// to perform a gated measurement, or they can be combined into even larger /// windows for a momentary loudness measurement. #[derive(Copy, Clone, Debug)] pub struct Windows100ms<T> { pub inner: T } impl<T> Windows100ms<T> { /// Wrap a new empty vector. pub fn new() -> Windows100ms<Vec<T>> { Windows100ms { inner: Vec::new(), } } /// Apply `as_ref` to the inner value. pub fn as_ref(&self) -> Windows100ms<&[Power]> where T: AsRef<[Power]> { Windows100ms { inner: self.inner.as_ref() } } /// Apply `as_mut` to the inner value. pub fn as_mut(&mut self) -> Windows100ms<&mut [Power]> where T: AsMut<[Power]> { Windows100ms { inner: self.inner.as_mut() } } /// Apply `len` to the inner value. pub fn len(&self) -> usize where T: AsRef<[Power]> { self.inner.as_ref().len() } } /// Measures K-weighted power of non-overlapping 100ms windows of a single channel of audio. /// /// # Output /// /// The output of the meter is an intermediate result in the form of power for /// 100ms non-overlapping windows. The windows need to be processed further to /// get one of the instantaneous, momentary, and integrated loudness /// measurements defined in BS.1770. /// /// The windows can also be inspected directly; the data is meaningful /// on its own (the K-weighted power delivered in that window of time), but it /// is not something that BS.1770 defines a term for. /// /// # Multichannel audio /// /// To perform a loudness measurement of multichannel audio, construct a /// `ChannelLoudnessMeter` per channel, and later combine the measured power /// with e.g. `reduce_stereo`. /// /// # Instantaneous loudness /// /// The instantaneous loudness is the power over a 400ms window, so you can /// average four 100ms windows. No special functionality is implemented to help /// with that at this time. ([Pull requests would be accepted.][contribute]) /// /// # Momentary loudness /// /// The momentary loudness is the power over a 3-second window, so you can /// average thirty 100ms windows. No special functionality is implemented to /// help with that at this time. ([Pull requests would be accepted.][contribute]) /// /// # Integrated loudness /// /// Use `gated_mean` to perform an integrated loudness measurement: /// /// ``` /// # use std::iter; /// # use bs1770::{ChannelLoudnessMeter, gated_mean}; /// # let sample_rate_hz = 44_100; /// # let samples_per_100ms = sample_rate_hz / 10; /// # let mut meter = ChannelLoudnessMeter::new(sample_rate_hz); /// # meter.push((0..44_100).map(|i| (i as f32 * 0.01).sin())); /// let integrated_loudness_lkfs = gated_mean(meter.as_100ms_windows()).loudness_lkfs(); /// ``` /// /// [contribute]: https://github.com/ruuda/bs1770/blob/master/CONTRIBUTING.md #[derive(Clone)] pub struct ChannelLoudnessMeter { /// The number of samples that fit in 100ms of audio. samples_per_100ms: u32, /// Stage 1 filter (head effects, high shelf). filter_stage1: Filter, /// Stage 2 filter (high-pass). filter_stage2: Filter, /// Sum of the squares over non-overlapping windows of 100ms. windows: Windows100ms<Vec<Power>>, /// The number of samples in the current unfinished window. count: u32, /// The sum of the squares of the samples in the current unfinished window. square_sum: Sum, } impl ChannelLoudnessMeter { /// Construct a new loudness meter for the given sample rate. pub fn new(sample_rate_hz: u32) -> ChannelLoudnessMeter { ChannelLoudnessMeter { samples_per_100ms: sample_rate_hz / 10, filter_stage1: Filter::high_shelf(sample_rate_hz as f32), filter_stage2: Filter::high_pass(sample_rate_hz as f32), windows: Windows100ms::new(), count: 0, square_sum: Sum::zero(), } } /// Feed input samples for loudness analysis. /// /// # Full scale /// /// Full scale for the input samples is the interval [-1.0, 1.0]. If your /// input consists of signed integer samples, you can convert as follows: /// /// ``` /// # let mut meter = bs1770::ChannelLoudnessMeter::new(44_100); /// # let bits_per_sample = 16_usize; /// # let samples = &[0_i16]; /// // Note that the maximum amplitude is `1 << (bits_per_sample - 1)`, /// // one bit is the sign bit. /// let normalizer = 1.0 / (1_u64 << (bits_per_sample - 1)) as f32; /// meter.push(samples.iter().map(|&s| s as f32 * normalizer)); /// ``` /// /// # Repeated calls /// /// You can call `push` multiple times to feed multiple batches of samples. /// This is equivalent to feeding a single chained iterator. The leftover of /// samples that did not fill a full 100ms window is not discarded: /// /// ``` /// # use std::iter; /// # use bs1770::ChannelLoudnessMeter; /// let sample_rate_hz = 44_100; /// let samples_per_100ms = sample_rate_hz / 10; /// let mut meter = ChannelLoudnessMeter::new(sample_rate_hz); /// /// meter.push(iter::repeat(0.0).take(samples_per_100ms as usize - 1)); /// assert_eq!(meter.as_100ms_windows().len(), 0); /// /// meter.push(iter::once(0.0)); /// assert_eq!(meter.as_100ms_windows().len(), 1); /// ``` pub fn push<I: Iterator<Item = f32>>(&mut self, samples: I) { let normalizer = 1.0 / self.samples_per_100ms as f32; // LLVM, if you could go ahead and inline those apply calls, and then // unroll and vectorize the loop, that'd be terrific. for x in samples { let y = self.filter_stage1.apply(x); let z = self.filter_stage2.apply(y); self.square_sum.add(z * z); self.count += 1; // TODO: Should this branch be marked cold? if self.count == self.samples_per_100ms { let mean_squares = Power(self.square_sum.sum * normalizer); self.windows.inner.push(mean_squares); // We intentionally do not reset the residue. That way, leftover // energy from this window is not lost, so for the file overall, // the sum remains more accurate. self.square_sum.sum = 0.0; self.count = 0; } } } /// Return a reference to the 100ms windows analyzed so far. pub fn as_100ms_windows(&self) -> Windows100ms<&[Power]> { self.windows.as_ref() } /// Return all 100ms windows analyzed so far. pub fn into_100ms_windows(self) -> Windows100ms<Vec<Power>> { self.windows } } /// Combine power for multiple channels by taking a weighted sum. /// /// Note that BS.1770-4 defines power for a multi-channel signal as a weighted /// sum over channels which is not normalized. This means that a stereo signal /// is inherently louder than a mono signal. For a mono signal played back on /// stereo speakers, you should therefore still apply `reduce_stereo`, passing /// in the same signal for both channels. pub fn reduce_stereo( left: Windows100ms<&[Power]>, right: Windows100ms<&[Power]>, ) -> Windows100ms<Vec<Power>> { assert_eq!(left.len(), right.len(), "Channels must have the same length."); let mut result = Vec::with_capacity(left.len()); for (l, r) in left.inner.iter().zip(right.inner) { result.push(Power(l.0 + r.0)); } Windows100ms { inner: result } } /// In-place version of `reduce_stereo` that stores the result in the former left channel. pub fn reduce_stereo_in_place( left: Windows100ms<&mut [Power]>, right: Windows100ms<&[Power]>, ) { assert_eq!(left.len(), right.len(), "Channels must have the same length."); for (l, r) in left.inner.iter_mut().zip(right.inner) { l.0 += r.0; } } /// Perform gating and averaging for a BS.1770-4 integrated loudness measurement. /// /// The integrated loudness measurement is not just the average power over the /// entire signal. BS.1770-4 defines defines two stages of gating that exclude /// parts of the signal, to ensure that silent parts do not contribute to the /// loudness measurment. This function performs that gating, and returns the /// average power over the windows that were not excluded. /// /// The result of this function is the integrated loudness measurement. pub fn gated_mean(windows_100ms: Windows100ms<&[Power]>) -> Power { let mut gating_blocks = Vec::with_capacity(windows_100ms.len()); // Stage 1: an absolute threshold of -70 LKFS. (Equation 6, p.6.) let absolute_threshold = Power::from_lkfs(-70.0); // Iterate over all 400ms windows. for window in windows_100ms.inner.windows(4) { // Note that the sum over channels has already been performed at this point. let gating_block_power = Power(0.25 * window.iter().map(|mean| mean.0).sum::<f32>()); if gating_block_power > absolute_threshold { gating_blocks.push(gating_block_power); } } // Compute the loudness after applying the absolute gate, in order to // determine the threshold for the relative gate. let mut sum_power = Sum::zero(); for &gating_block_power in &gating_blocks { sum_power.add(gating_block_power.0); } let absolute_gated_power = Power(sum_power.sum / (gating_blocks.len() as f32)); // Stage 2: Apply the relative gate. let relative_threshold = Power::from_lkfs(absolute_gated_power.loudness_lkfs() - 10.0); let mut sum_power = Sum::zero(); let mut n_blocks = 0_usize; for &gating_block_power in &gating_blocks { if gating_block_power > relative_threshold { sum_power.add(gating_block_power.0); n_blocks += 1; } } let relative_gated_power = Power(sum_power.sum / n_blocks as f32); relative_gated_power } #[cfg(test)] mod tests { use super::{ChannelLoudnessMeter, Filter, Power}; use super::{reduce_stereo, gated_mean}; #[test] fn filter_high_shelf_matches_spec() { // Test that the computed coefficients match those in table 1 of the // spec (page 4 of BS.1770-4). let sample_rate_hz = 48_000.0; let f = Filter::high_shelf(sample_rate_hz); assert!((f.a1 - -1.69065929318241).abs() < 1e-6); assert!((f.a2 - 0.73248077421585).abs() < 1e-6); assert!((f.b0 - 1.53512485958697).abs() < 1e-6); assert!((f.b1 - -2.69169618940638).abs() < 1e-6); assert!((f.b2 - 1.19839281085285).abs() < 1e-6); } #[test] fn filter_low_pass_matches_spec() { // Test that the computed coefficients match those in table 1 of the // spec (page 4 of BS.1770-4). let sample_rate_hz = 48_000.0; let f = Filter::high_pass(sample_rate_hz); assert!((f.a1 - -1.99004745483398).abs() < 1e-6); assert!((f.a2 - 0.99007225036621).abs() < 1e-6); assert!((f.b0 - 1.0).abs() < 1e-6); assert!((f.b1 - -2.0).abs() < 1e-6); assert!((f.b2 - 1.0).abs() < 1e-6); } fn append_pure_tone( samples: &mut Vec<f32>, sample_rate_hz: usize, frequency_hz: usize, duration_milliseconds: usize, amplitude_dbfs: f32, ) { use std::f32; let num_samples = (duration_milliseconds * sample_rate_hz) / 1000; samples.reserve(num_samples); let sample_duration_seconds = 1.0 / (sample_rate_hz as f32); let amplitude = 10.0_f32.powf(amplitude_dbfs / 20.0); for i in 0..num_samples { let time_seconds = i as f32 * sample_duration_seconds; let angle = f32::consts::PI * 2.0 * time_seconds * frequency_hz as f32; samples.push(angle.sin() * amplitude); } } fn assert_loudness_in_range_lkfs( power: Power, target_lkfs: f32, plusminus_lkfs: f32, context: &str, ) { assert!( power.loudness_lkfs() > target_lkfs - plusminus_lkfs, "Actual loudness of {:.1} LKFS too low for reference {:.1} ± {:.1} LKFS at {}", power.loudness_lkfs(), target_lkfs, plusminus_lkfs, context, ); assert!( power.loudness_lkfs() < target_lkfs + plusminus_lkfs, "Actual loudness of {:.1} LKFS too high for reference {:.1} ± {:.1} LKFS at {}", power.loudness_lkfs(), target_lkfs, plusminus_lkfs, context, ); } #[test] fn loudness_matches_tech_3341_2016_case_1_and_2() { // Case 1 and 2 on p.10 of EBU Tech 3341-2016, a stereo sine wave of // 1000 Hz at -23.0 dBFS and -33.0 dBFS for 20 seconds. let sample_rates = [44_100, 48_000, 96_000, 192_000]; let amplitudes = [-23.0, -33.0]; for &sample_rate_hz in &sample_rates { for &litude_dbfs in &litudes { let mut samples = Vec::new(); let frequency_hz = 1_000; let duration_milliseconds = 20_000; append_pure_tone( &mut samples, sample_rate_hz, frequency_hz, duration_milliseconds, amplitude_dbfs, ); let mut meter = ChannelLoudnessMeter::new(sample_rate_hz as u32); meter.push(samples.iter().cloned()); // The reference specifies a stereo signal with the same contents in // both channels. let windows_single = meter.as_100ms_windows(); let windows_stereo = reduce_stereo(windows_single, windows_single); let power = gated_mean(windows_stereo.as_ref()); assert_loudness_in_range_lkfs( power, amplitude_dbfs, 0.1, &format!( "sample_rate: {} Hz, amplitude: {:.1} dBFS", sample_rate_hz, amplitude_dbfs, ), ); } } } #[test] fn loudness_matches_tech_3341_2016_case_3_and_4_and_5() { // Case 3, 4, and 5 on p.10 of EBU Tech 3341-2016. Their expected // outputs are the same, but the tones are different. let sample_rates = [44_100, 48_000, 96_000, 192_000]; let tones_duration_milliseconds_amplitude_dbfs = [ &[ (10_000, -36.0), (60_000, -23.0), (10_000, -36.0), ][..], &[ (10_000, -72.0), (10_000, -36.0), (60_000, -23.0), (10_000, -36.0), (10_000, -72.0), ][..], &[ (20_000, -26.0), (20_100, -20.0), (20_000, -26.0), ][..], ]; for &sample_rate_hz in &sample_rates { for (i, &test_case) in tones_duration_milliseconds_amplitude_dbfs.iter().enumerate() { let mut meter = ChannelLoudnessMeter::new(sample_rate_hz as u32); let mut samples = Vec::new(); let frequency_hz = 1_000; for &(duration_milliseconds, amplitude_dbfs) in test_case.iter() { append_pure_tone( &mut samples, sample_rate_hz, frequency_hz, duration_milliseconds, amplitude_dbfs, ); } meter.push(samples.iter().cloned()); let windows_single = meter.as_100ms_windows(); let windows_stereo = reduce_stereo(windows_single.as_ref(), windows_single.as_ref()); let power = gated_mean(windows_stereo.as_ref()); assert_loudness_in_range_lkfs( power, -23.0, 0.1, &format!( "sample_rate: {} Hz, case {}", sample_rate_hz, i + 3 ), ); } } } /// Analyze a single channel of a wave file. /// /// This is a bit inefficient because we have to read the file twice to get /// all channels, but it is simple to implement. fn analyze_wav_channel(fname: &str, channel: usize) -> ChannelLoudnessMeter { let mut reader = hound::WavReader::open(fname) .expect("Failed to open reference file, run ./download_test_data.sh to download it."); let spec = reader.spec(); // The maximum amplitude is 1 << (bits per sample - 1), because one bit // is the sign bit. let normalizer = 1.0 / (1_u64 << (spec.bits_per_sample - 1)) as f32; // Step the sampes by 2, because the audio is stereo, skipping `channel` // at the start to ensure that we select the right channel. let channel_samples = reader .samples() .skip(channel) .step_by(2) .map(|s: hound::Result<i32>| s.unwrap() as f32 * normalizer); let mut meter = ChannelLoudnessMeter::new(spec.sample_rate); meter.push(channel_samples); meter } fn test_stereo_reference_file(fname: &str) { let windows_ch0 = analyze_wav_channel(fname, 0).into_100ms_windows(); let windows_ch1 = analyze_wav_channel(fname, 1).into_100ms_windows(); let windows_stereo = reduce_stereo(windows_ch0.as_ref(), windows_ch1.as_ref()); let power = gated_mean(windows_stereo.as_ref()); // All of the reference samples have the same expected loudness of // -23 LKFS. assert_loudness_in_range_lkfs(power, -23.0, 0.1, fname); } #[test] fn loudness_matches_tech_3341_2016_case_7() { test_stereo_reference_file("tech_3341_test_case_7.wav"); } #[test] fn loudness_matches_tech_3341_2016_case_8() { test_stereo_reference_file("tech_3341_test_case_8.wav"); } }