spectrum-analyzer 2.0.0

/*
MIT License

Copyright (c) 2023 Philipp Schuster

Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.
*/
//! Several window functions which you can apply before doing the FFT.
//! For more information:
//! - <https://en.wikipedia.org/wiki/Window_function>
//! - <https://www.youtube.com/watch?v=dCeHOf4cJE0> (FFT and windowing by Texas Instruments)
//!
//! A window reduces spectral leakage: without one, a frequency that does not
//! fit a whole number of times into the block smears over the whole spectrum
//! and can bury quieter frequencies. Applying one is almost always the right
//! choice.
//!
//! ## Which window should I use?
//! * [`hann_window`]: the default. A good compromise, use it unless you have
//!   a reason not to.
//! * [`hamming_window`]: close to Hann, with slightly different trade-offs
//!   between near and distant leakage.
//! * [`blackman_harris_4term`]: when a quiet frequency sits next to a loud
//!   one. It suppresses distant leakage much more, at the price of lower and
//!   wider peaks.
//! * [`blackman_harris_7term`]: the same idea taken further. Rarely needed.
//!
//! Skipping the window only makes sense if every frequency fits a whole
//! number of times into the block, which in practice means synthetic signals.
//!
//! ## Periodic and symmetric windows
//! Every window comes in two variants that differ in a single value. NumPy
//! and SciPy build the *symmetric* one by default, which is made for filter
//! design. This crate uses the *periodic* one, the variant for FFT analysis,
//! which also makes the coherent gain below exact.
//!
//! You only notice the difference when comparing coefficients with another
//! library: for `N` values, the periodic variant is the symmetric one for
//! `N + 1` values with the last value cut off. See [conventions] on
//! Wikipedia and the `sym` parameter in [SciPy].
//!
//! Every window shrinks the values in the spectrum by a constant factor, its
//! coherent gain (the average of its coefficients, i.e., the first
//! coefficient of the cosine sum). Divide by it to undo the
//! effect, see [`crate::samples_fft_to_spectrum`].
//!
//! [conventions]: https://en.wikipedia.org/wiki/Window_function#Conventions
//! [SciPy]: https://docs.scipy.org/doc/scipy/reference/generated/scipy.signal.windows.hann.html

use alloc::vec::Vec;
use core::f32::consts::PI;
// replacement for std functions like sin and cos in no_std-environments
use libm::cosf;

/// Applies a Hann window (<https://en.wikipedia.org/wiki/Window_function#Hann_and_Hamming_windows>)
/// to an array of samples.
///
/// Coherent gain: `0.5`, i.e., the values in the spectrum are halved.
///
/// See the [module docs](crate::windows) for picking a window function.
///
/// ## Return value
/// New vector with Hann window applied to the values.
#[must_use]
pub fn hann_window(samples: &[f32]) -> Vec<f32> {
    let mut windowed_samples = Vec::with_capacity(samples.len());
    let samples_len_f32 = samples.len() as f32;
    for (i, sample) in samples.iter().enumerate() {
        let two_pi_i = 2.0 * PI * i as f32;
        let idontknowthename = cosf(two_pi_i / samples_len_f32);
        let multiplier = 0.5 * (1.0 - idontknowthename);
        windowed_samples.push(multiplier * sample)
    }
    windowed_samples
}

/// Applies a Hamming window (<https://en.wikipedia.org/wiki/Window_function#Hann_and_Hamming_windows>)
/// to an array of samples.
///
/// Coherent gain: `0.54`.
///
/// See the [module docs](crate::windows) for picking a window function.
///
/// ## Return value
/// New vector with Hamming window applied to the values.
#[must_use]
pub fn hamming_window(samples: &[f32]) -> Vec<f32> {
    let mut windowed_samples = Vec::with_capacity(samples.len());
    let samples_len_f32 = samples.len() as f32;
    for (i, sample) in samples.iter().enumerate() {
        let multiplier = 0.54 - (0.46 * cosf(2.0 * PI * i as f32 / samples_len_f32));
        windowed_samples.push(multiplier * sample)
    }
    windowed_samples
}

/// Applies a Blackman-Harris 4-term window (<https://en.wikipedia.org/wiki/Window_function#Blackman%E2%80%93Harris_window>)
/// to an array of samples.
///
/// Coherent gain: `0.35875`.
///
/// See the [module docs](crate::windows) for picking a window function.
///
/// ## Return value
/// New vector with Blackman-Harris 4-term window applied to the values.
#[must_use]
pub fn blackman_harris_4term(samples: &[f32]) -> Vec<f32> {
    // constants come from here:
    // https://en.wikipedia.org/wiki/Window_function#Blackman%E2%80%93Harris_window
    const ALPHA: [f32; 4] = [0.35875, -0.48829, 0.14128, -0.01168];

    blackman_harris_xterm(samples, &ALPHA)
}

/// Applies a Blackman-Harris 7-term window to an array of samples.
///
/// Coherent gain: `0.2710514`.
///
/// See the [module docs](crate::windows) for picking a window function.
///
/// ## More information
/// * <https://en.wikipedia.org/wiki/Window_function#Blackman%E2%80%93Harris_window>
/// * <https://ieeexplore.ieee.org/document/940309>
/// * <https://dsp.stackexchange.com/questions/51095/seven-term-blackman-harris-window>
///
/// ## Return value
/// New vector with Blackman-Harris 7-term window applied to the values.
#[must_use]
pub fn blackman_harris_7term(samples: &[f32]) -> Vec<f32> {
    // constants come from here:
    // https://dsp.stackexchange.com/questions/51095/seven-term-blackman-harris-window
    const ALPHA: [f32; 7] = [
        0.271_051_4,
        -0.433_297_93,
        0.218_123,
        -0.065_925_45,
        0.010_811_742,
        -0.000_776_584_84,
        0.000_013_887_217,
    ];

    blackman_harris_xterm(samples, &ALPHA)
}

/// Applies a Blackman-Harris x-term window
/// (<https://en.wikipedia.org/wiki/Window_function#Blackman%E2%80%93Harris_window>)
/// to an array of samples. The x is specified by `alphas.len()`.
///
/// ## Return value
/// New vector with Blackman-Harris x-term window applied to the values.
#[must_use]
fn blackman_harris_xterm(samples: &[f32], alphas: &[f32]) -> Vec<f32> {
    let mut windowed_samples = Vec::with_capacity(samples.len());
    let samples_len_f32 = samples.len() as f32;

    for (i, sample) in samples.iter().enumerate() {
        // Will result in something like that:
        /* ALPHA0
            + ALPHA1 * ((2.0 * PI * i)/samples_len_f32).cos()
            + ALPHA2 * ((4.0 * PI * i)/samples_len_f32).cos()
            + ALPHA3 * ((6.0 * PI * i)/samples_len_f32).cos()
        */

        let mut acc = 0.0;
        for (alpha_i, alpha) in alphas.iter().enumerate() {
            // in 1. iter. 0PI, then 2PI, then 4 PI, then 6 PI
            let two_pi_iteration = 2.0 * alpha_i as f32 * PI;
            let cos = cosf((two_pi_iteration * i as f32) / samples_len_f32);
            acc += alpha * cos;
        }

        windowed_samples.push(acc * sample)
    }

    windowed_samples
}

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

    #[test]
    fn test_hamming_window_coefficients() {
        let windowed = hamming_window(&[1.0; 4]);
        let expected = [0.08, 0.54, 1.0, 0.54];

        for (actual, expected) in windowed.iter().zip(expected) {
            float_cmp::assert_approx_eq!(f32, *actual, expected, epsilon = 0.00001);
        }
    }

    #[test]
    fn test_blackman_harris_4term_window_coefficients() {
        let windowed = blackman_harris_4term(&[2.0; 4]);
        let expected = [0.00012, 0.43494, 2.0, 0.43494];

        for (actual, expected) in windowed.iter().zip(expected) {
            float_cmp::assert_approx_eq!(f32, *actual, expected, epsilon = 0.00001);
        }
    }
}