spectrum_analyzer/

scaling.rs

/*
MIT License

Copyright (c) 2023 Philipp Schuster

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*/
//! This module contains convenient public transform functions that you can use
//! as parameters in [`samples_fft_to_spectrum`] for scaling the frequency value
//! (the FFT result).
//!
//! ## Which scaling should I use?
//! * [`divide_by_N`]: the default. It makes the values independent of the
//!   number of samples, so spectra of different lengths are comparable.
//! * [`scale_20_times_log10`]: decibels, for a display that should match how
//!   loudness is perceived.
//! * [`scale_to_zero_to_one`]: for a single block where only the relative
//!   height of the peaks matters, e.g. a plot or a test. Avoid it for a live
//!   view: it normalises every block to its own loudest value, so silence
//!   gets amplified to full scale.
//! * [`divide_by_N_sqrt`]: preserves the energy of the signal, for a forward
//!   and inverse transform pair.
//! * None at all is fine if you only compare values within one spectrum, for
//!   example to find the loudest frequency.
//!
//! To read the amplitude of a tone, use [`divide_by_N`], multiply by `2` and
//! divide by the coherent gain of your window, see
//! [`crate::samples_fft_to_spectrum`].
//!
//! They act as "idea/inspiration". Feel free to create your own derivation
//! from them. To chain two of them, write a closure:
//!
//! ```
//! use spectrum_analyzer::scaling::{divide_by_N, scale_20_times_log10};
//! let scaling_fn = |val, stats: &_| scale_20_times_log10(divide_by_N(val, stats), stats);
//! ```
//!
//! [`samples_fft_to_spectrum`]: crate::samples_fft_to_spectrum

use crate::FrequencyValue;

/// Helper struct for [`SpectrumScalingFunction`] that is passed into the
/// scaling function together with the current frequency value.
///
/// This structure can be used to scale each value. All properties reference the
/// current data of a [`FrequencySpectrum`].
///
/// [`FrequencySpectrum`]: crate::FrequencySpectrum
/// [`FrequencyValue`]: crate::FrequencyValue
#[derive(Debug)]
pub struct SpectrumDataStats {
    /// Minimal frequency value in spectrum.
    pub min: FrequencyValue,
    /// Maximum frequency value in spectrum.
    pub max: FrequencyValue,
    /// Average frequency value in spectrum.
    pub average: FrequencyValue,
    /// Number of samples (`samples.len()`), not the number of values in the
    /// spectrum (which can be smaller due to a frequency limit).
    pub n: f32,
}

/// Describes the type for a function that scales/normalizes the data inside
/// [`FrequencySpectrum`].
///
/// The scaling only affects the value of the frequency, but not the
/// frequency itself. It is applied to every single element.
///
/// A scaling function can be used for example to subtract the minimum (`min`)
/// from each value. It is optional to use the second parameter
/// [`SpectrumDataStats`], which describes the spectrum before the function is
/// applied to it.
///
/// The type works with static functions as well as dynamically created
/// closures.
///
/// You must take care of, that you don't have division by zero in your function
/// or that the result is NaN or Infinity (regarding IEEE-754). If the result
/// is NaN or Infinity, the library will return `Err`.
///
/// [`FrequencySpectrum`]: crate::FrequencySpectrum
/// [`FrequencyValue`]: crate::FrequencyValue
pub type SpectrumScalingFunction = dyn Fn(f32, &SpectrumDataStats) -> f32;

/// Lower bound for the input of [`scale_20_times_log10`], i.e., `-100 dB`.
const DB_FLOOR: f32 = 1e-5;

/// Converts each value to decibels: `20 * log10(value)`.
///
/// See the [module docs](crate::scaling) for picking a scaling function.
///
/// A value of `1.0` becomes `0 dB`. Unscaled values grow with the number of
/// samples (see [`crate::samples_fft_to_spectrum`]), so the absolute levels
/// depend on `N` and on the input range. For levels relative to a full-scale
/// sine wave (dBFS), scale to amplitudes first, in a separate call to
/// `apply_scaling_fn`.
///
/// Values below `1e-5` are clamped, so the result is never below `-100 dB`
/// and silence stays at the bottom of the scale.
///
/// This scaling is quite common, you can find more information for example
/// here:
/// <https://www.sjsu.edu/people/burford.furman/docs/me120/FFT_tutorial_NI.pdf>
///
/// ## Usage
/// ```rust
///use spectrum_analyzer::{samples_fft_to_spectrum, scaling, FrequencyLimit};
///let window = [0.0, 0.1, 0.2, 0.3]; // add real data here
///let spectrum = samples_fft_to_spectrum(
///     &window,
///     44100,
///     FrequencyLimit::All,
///     Some(&scaling::scale_20_times_log10),
/// );
/// ```
/// Function is of type [`SpectrumScalingFunction`].
#[must_use]
pub fn scale_20_times_log10(fr_val: f32, _stats: &SpectrumDataStats) -> f32 {
    debug_assert!(!fr_val.is_infinite());
    debug_assert!(!fr_val.is_nan());
    debug_assert!(fr_val >= 0.0);
    // Clamping keeps silence below every other value (0 dB would not).
    20.0 * libm::log10f(fr_val.max(DB_FLOOR))
}

/// Divides each value by the maximum, so that the loudest frequency becomes
/// `1.0` and every other keeps its ratio to it.
///
/// See the [module docs](crate::scaling) for picking a scaling function.
///
/// The smallest value only becomes `0.0` if it already was `0.0`; the values
/// are not stretched over the whole interval. All of them must be positive or
/// zero, which holds for magnitudes but not for the output of
/// [`scale_20_times_log10`]. If the maximum is `0.0`, all values become `0.0`.
///
/// Function is of type [`SpectrumScalingFunction`].
#[must_use]
pub fn scale_to_zero_to_one(fr_val: f32, stats: &SpectrumDataStats) -> f32 {
    debug_assert!(!fr_val.is_infinite());
    debug_assert!(!fr_val.is_nan());
    debug_assert!(fr_val >= 0.0);
    if stats.max != 0.0 {
        fr_val / stats.max
    } else {
        0.0
    }
}

/// Divides each value by `N`, the number of samples.
///
/// See the [module docs](crate::scaling) for picking a scaling function.
///
/// This makes spectra of different lengths comparable. A sine wave with
/// amplitude `A` on a bin frequency then shows up as `A / 2` (times the
/// window's coherent gain), see [`crate::samples_fft_to_spectrum`].
#[allow(non_snake_case)]
#[must_use]
pub fn divide_by_N(fr_val: f32, stats: &SpectrumDataStats) -> f32 {
    debug_assert!(!fr_val.is_infinite());
    debug_assert!(!fr_val.is_nan());
    debug_assert!(fr_val >= 0.0);
    if stats.n == 0.0 {
        fr_val
    } else {
        fr_val / stats.n
    }
}

/// Like [`divide_by_N`] but divides each value by `sqrt(N)`.
///
/// See the [module docs](crate::scaling) for picking a scaling function.
///
/// This is the normalization that preserves the energy of the signal, which
/// `rustfft` recommends for a forward and inverse transform pair. The values
/// still grow with `sqrt(N)`, so for comparing spectra of different lengths
/// use [`divide_by_N`] instead.
/// See <https://docs.rs/rustfft/latest/rustfft/#normalization>
#[allow(non_snake_case)]
#[must_use]
pub fn divide_by_N_sqrt(fr_val: f32, stats: &SpectrumDataStats) -> f32 {
    debug_assert!(!fr_val.is_infinite());
    debug_assert!(!fr_val.is_nan());
    debug_assert!(fr_val >= 0.0);
    if stats.n == 0.0 {
        fr_val
    } else {
        // https://docs.rs/rustfft/latest/rustfft/#normalization
        fr_val / libm::sqrtf(stats.n)
    }
}

#[cfg(test)]
mod tests {
    use super::*;
    use alloc::vec::Vec;

    #[test]
    fn test_scale_to_zero_to_one() {
        let data = vec![0.0_f32, 1.1, 2.2, 3.3, 4.4, 5.5];
        let stats = SpectrumDataStats {
            min: data[0].into(),
            max: data[data.len() - 1].into(),
            average: (data.iter().sum::<f32>() / data.len() as f32).into(),
            n: data.len() as f32,
        };
        // check that type matches
        let scaling_fn: &SpectrumScalingFunction = &scale_to_zero_to_one;
        let scaled_data = data
            .into_iter()
            .map(|x| scaling_fn(x, &stats))
            .collect::<Vec<_>>();
        let expected = [0.0_f32, 0.2, 0.4, 0.6, 0.8, 1.0];
        for (expected_val, actual_val) in expected.iter().zip(scaled_data.iter()) {
            float_cmp::approx_eq!(f32, *expected_val, *actual_val, ulps = 3);
        }
    }

    #[test]
    fn test_scale_20_times_log10() {
        let stats = SpectrumDataStats {
            min: 0.0.into(),
            max: 10.0.into(),
            average: 0.0.into(),
            n: 4.0,
        };
        let db = |val: f32| scale_20_times_log10(val, &stats);
        assert!(float_cmp::approx_eq!(f32, db(1.0), 0.0, epsilon = 1e-4));
        assert!(float_cmp::approx_eq!(f32, db(10.0), 20.0, epsilon = 1e-4));
        assert!(float_cmp::approx_eq!(f32, db(0.0), -100.0, epsilon = 1e-3));
        // silence must stay below every other value
        assert!(db(0.0) < db(0.5) && db(0.5) < db(1.0));
    }

    /// A closure replaces the removed `combined()`: it can chain the
    /// functions and, unlike `combined()`, capture its environment.
    #[test]
    fn test_chaining_with_a_closure() {
        let stats = SpectrumDataStats {
            min: 0.0.into(),
            max: 10.0.into(),
            average: 5.0.into(),
            n: 4.0,
        };
        let scaling_fn = |val, stats: &_| scale_20_times_log10(divide_by_N(val, stats), stats);
        let _: &SpectrumScalingFunction = &scaling_fn;
        // 10.0 / 4 = 2.5 -> 20 * log10(2.5)
        assert!(float_cmp::approx_eq!(
            f32,
            scaling_fn(stats.max.val(), &stats),
            7.9588,
            epsilon = 1e-3
        ));
    }
}