dsp 0.11.0

Digital Signal Processing
Documentation 
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//! Standard Windows functions

use std::f32::consts::PI;
use crate::vector;


/// A window function. Can be applied to a signal
#[derive(Clone, Debug, PartialEq)]
pub struct Window {
    pub samples: Vec<f32>,
}

impl Window {
    /// Returns the length of the window, in frames
    pub fn len(&self) -> usize {
        self.samples.len()
    }

    /// Apply this window to the given frame
    pub fn apply(&self, input: &[f32], mut output: &mut [f32]) {
        vector::multiply(&self.samples, &input, &mut output);
    }

    pub fn as_slice(&self) -> &[f32] {
        &self.samples
    }
}


/// Compute a simple rectangular window, a.k.a. __boxcar__ or __Dirichlet__ window
/// 
/// Example
/// 
/// ```
/// use dsp::window;
/// 
/// let win = window::rectangular(3);
/// let frame = vec![1.0; 3];
/// let mut output = vec![0.0; 3];
/// win.apply(&frame, &mut output);
/// assert_eq!(output, vec![1.0, 1.0, 1.0]);
/// ```
pub fn rectangular(width: usize) -> Window {
    let mut samples = vec![0.0; width];
    for i in 0..width {
        samples[i] = 1.0;    
    }
    Window { samples }
}

/// Creates a triangular window
/// 
/// Example
/// 
/// ```
/// use dsp::window;
/// 
/// let win = window::triangular(5);
/// let frame = vec![1.0; 5];
/// let mut output = vec![0.0; 5];
/// win.apply(&frame, &mut output);
/// assert_eq!(output, vec![0.0, 0.5, 1.0, 0.5, 0.0]);
/// ```
pub fn triangular(width: usize) -> Window {
    let mut samples = vec![0.0; width];
    let slope = 2.0 / ((width - 1) as f32);
    for i in 0..width {
        let y = i as f32 * slope;
        samples[i] = if i < width / 2 { y } else { 2.0 - y }    
    }
    Window { samples }
}

/// Create the Welch window
/// https://en.wikipedia.org/wiki/Window_function#Welch_window
/// 
/// Example
/// 
/// ```
/// use dsp::window;
/// 
/// let win = window::welch(5);
/// let frame = vec![1.0; 5];
/// let mut output = vec![0.0; 5];
/// win.apply(&frame, &mut output);
/// assert_eq!(output, vec![0.0, 0.75, 1.0, 0.75, 0.0]);
/// ```
pub fn welch(width: usize) -> Window {
    let mut samples = vec![0.0; width];
    let half_width = (width-1) as f32 / 2.0;
    for i in 0..width {
        let n = i as f32;
        let y = 1.0 - ((n - half_width) / half_width).powi(2);
        samples[i] = y as f32;
    }
    Window { samples }
}

/// Create the Sine window
/// https://en.wikipedia.org/wiki/Window_function#Sine_window
/// 
/// Example
/// 
/// ```
/// use assert_approx_eq::assert_approx_eq;
/// use dsp::window;
/// 
/// let win = window::sine(5);
/// let frame = vec![1.0; 5];
/// let mut output = vec![0.0; 5];
/// win.apply(&frame, &mut output);
/// assert_approx_eq!(output[0], 0.0, 1e-5f32);
/// assert_approx_eq!(output[1], 0.707, 1e-3f32);
/// assert_approx_eq!(output[2], 1.0, 1e-3f32);
/// assert_approx_eq!(output[3], 0.707, 1e-3f32);
/// assert_approx_eq!(output[4], 0.0, 1e-5f32);
/// ```
pub fn sine(width: usize) -> Window {
    let mut samples = vec![0.0; width];
    for i in 0..width {
        let n = i as f32;
        samples[i] = (PI * n / (width - 1) as f32).sin();
    }
    Window { samples }
}

/// Create the Hann window
/// https://en.wikipedia.org/wiki/Window_function#Hann_and_Hamming_window
/// 
/// Example
/// 
/// ```
/// use assert_approx_eq::assert_approx_eq;
/// use dsp::window;
/// 
/// let win = window::hann(5);
/// let frame = vec![1.0; 5];
/// let mut output = vec![0.0; 5];
/// win.apply(&frame, &mut output);
/// assert_approx_eq!(output[0], 0.0, 1e-5f32);
/// assert_approx_eq!(output[1], 0.5, 1e-3f32);
/// assert_approx_eq!(output[2], 1.0, 1e-3f32);
/// assert_approx_eq!(output[3], 0.5, 1e-3f32);
/// assert_approx_eq!(output[4], 0.0, 1e-5f32);
/// ```
pub fn hann(width: usize) -> Window {
    let mut samples = vec![0.0; width];
    for i in 0..width {
        let n = i as f32;
        samples[i] = (PI * n / (width - 1) as f32).sin().powi(2);
    }
    Window { samples }
}

/// Compute a hamming window of the given size
/// https://en.wikipedia.org/wiki/Window_function#Hann_and_Hamming_window
/// 
/// Example
/// 
/// ```
/// use assert_approx_eq::assert_approx_eq;
/// use dsp::window;
/// 
/// let win = window::hamming(5);
/// let frame = vec![1.0; 5];
/// let mut output = vec![0.0; 5];
/// win.apply(&frame, &mut output);
/// assert_approx_eq!(output[0], 0.0869, 1e-3f32);
/// assert_approx_eq!(output[1], 0.54347825, 1e-3f32);
/// assert_approx_eq!(output[2], 1.0, 1e-3f32);
/// assert_approx_eq!(output[3], 0.54347825, 1e-3f32);
/// assert_approx_eq!(output[4], 0.0869, 1e-3f32);
/// ```
pub fn hamming(width: usize) -> Window {
    let a0 = 25.0 / 46.0;
    let mut samples = vec![0.0; width];
    let size = (width - 1) as f32;
    for i in 0..width {
        let n = i as f32;
        let v = a0 - (1.0 - a0) * (2.0 * PI * n / size).cos();
        samples[i] = v;
    }
    Window { samples }
}

/// Compute a Blackman window
/// https://en.wikipedia.org/wiki/Window_function#Blackman_window
/// 
/// Example
/// 
/// ```
/// use assert_approx_eq::assert_approx_eq;
/// use dsp::window;
/// 
/// let win = window::blackman(5);
/// let frame = vec![1.0; 5];
/// let mut output = vec![0.0; 5];
/// win.apply(&frame, &mut output);
/// assert_approx_eq!(output[0], 0.00687, 1e-5f32);
/// assert_approx_eq!(output[1], 0.34974, 1e-5f32);
/// assert_approx_eq!(output[2], 1.0, 1e-5f32);
/// assert_approx_eq!(output[3], 0.34974, 1e-5f32);
/// assert_approx_eq!(output[4], 0.00687, 1e-5f32);
/// ```
pub fn blackman(width: usize) -> Window {
    let a0 = 7938.0 / 18608.0;
    let a1 = 9240.0 / 18608.0;
    let a2 = 1430.0 / 18608.0;
    let mut samples = vec![0.0; width];
    let size = (width - 1) as f32;
    for i in 0..width {
        let n = i as f32;
        let v = a0 - a1 * (2.0 * PI * n / size).cos()
                    + a2 * (4.0 * PI * n / size).cos();
        samples[i] = v;
    }
    Window { samples }
}

/// ------------------------------------------------------------------------------------------------
/// Module unit tests
/// ------------------------------------------------------------------------------------------------
#[cfg(test)]
mod tests {

    use assert_approx_eq::assert_approx_eq;
    use super::*;

    #[test]
    fn test_window() {
        let win = rectangular(3);
        let frame = vec![1.0; 3];
        let mut output = vec![0.0; 3];
        win.apply(&frame, &mut output);
        assert_eq!(output, vec![1.0, 1.0, 1.0]);
    }

    #[test]
    fn test_apply() {
        let w = triangular(1000);
        let frame = vec![1.0; 1000];
        let mut output = vec![0.0; 1000];

        w.apply(&frame, &mut output);
        let area: f32 = output.iter().sum();
        assert_approx_eq!(area / 1000.0, 0.5, 0.2);
    }
}