1
  2
  3
  4
  5
  6
  7
  8
  9
 10
 11
 12
 13
 14
 15
 16
 17
 18
 19
 20
 21
 22
 23
 24
 25
 26
 27
 28
 29
 30
 31
 32
 33
 34
 35
 36
 37
 38
 39
 40
 41
 42
 43
 44
 45
 46
 47
 48
 49
 50
 51
 52
 53
 54
 55
 56
 57
 58
 59
 60
 61
 62
 63
 64
 65
 66
 67
 68
 69
 70
 71
 72
 73
 74
 75
 76
 77
 78
 79
 80
 81
 82
 83
 84
 85
 86
 87
 88
 89
 90
 91
 92
 93
 94
 95
 96
 97
 98
 99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183

//! This mod contains a definition for window functions and provides implementations for a
//! few standard windows. See the `WindowFunction` type for more information.
use crate::numbers::*;

/// A window function for FFT windows. See `https://en.wikipedia.org/wiki/Window_function`
/// for details. Window functions should document if they aren't applicable for
/// Inverse Fourier Transformations.
///
/// The contract for window functions is as follows:
///
/// 1. The second argument is of the function is always `vector.points()` and the possible values
///    for the first argument ranges from `0..vector.points()`.
/// 2. All real return values are allowed
pub trait WindowFunction<T>: Sync
where
    T: RealNumber,
{
    /// Indicates whether this function is symmetric around the y axis or not.
    /// Symmetry is defined as `self.window(x) == self.window(-x)`.
    fn is_symmetric(&self) -> bool;

    /// Calculates a point of the window function. Callers will ensure that `n <= length`.
    fn window(&self, n: usize, length: usize) -> T;
}

/// A triangular window: <https://en.wikipedia.org/wiki/Window_function#Triangular_window>
pub struct TriangularWindow;
impl<T> WindowFunction<T> for TriangularWindow
where
    T: RealNumber,
{
    fn is_symmetric(&self) -> bool {
        true
    }

    fn window(&self, n: usize, length: usize) -> T {
        let one = T::one();
        let two = T::from(2.0).unwrap();
        let n = T::from(n).unwrap();
        let length = T::from(length).unwrap();
        one - ((n - (length - one) / two) / (length / two)).abs()
    }
}

/// A generalized Hamming window: <https://en.wikipedia.org/wiki/Window_function#Hamming_window>
pub struct HammingWindow<T>
where
    T: RealNumber,
{
    alpha: T,
    beta: T,
}

impl<T> HammingWindow<T>
where
    T: RealNumber,
{
    /// Creates a new Hamming window
    pub fn new(alpha: T) -> Self {
        HammingWindow {
            alpha,
            beta: (T::one() - alpha),
        }
    }

    /// Creates the default Hamming window as defined in GNU Octave.
    pub fn default() -> Self {
        Self::new(T::from(0.54).unwrap())
    }
}

impl<T> WindowFunction<T> for HammingWindow<T>
where
    T: RealNumber,
{
    fn is_symmetric(&self) -> bool {
        true
    }

    fn window(&self, n: usize, length: usize) -> T {
        let one = T::one();
        let two = T::from(2.0).unwrap();
        let pi = T::PI();
        let n = T::from(n).unwrap();
        let length = T::from(length).unwrap();
        self.alpha - self.beta * (two * pi * n / (length - one)).cos()
    }
}

/// A Blackman-Harris Window: <https://en.wikipedia.org/wiki/Window_function#Blackman-Harris_window>
pub struct BlackmanHarrisWindow;
impl<T> WindowFunction<T> for BlackmanHarrisWindow
where
    T: RealNumber,
{
    fn is_symmetric(&self) -> bool {
        true
    }

    fn window(&self, n: usize, length: usize) -> T {
        let one = T::one();
        let two = T::from(2.0).unwrap();
        let four = T::from(4.0).unwrap();
        let six = T::from(6.0).unwrap();
        let pi = T::PI();
        let a_naught = T::from(0.35875).unwrap();
        let a_one = T::from(0.48829).unwrap();
        let a_two = T::from(0.14128).unwrap();
        let a_three = T::from(0.01168).unwrap();
        let n = T::from(n).unwrap();
        let length = T::from(length).unwrap();
        a_naught - a_one * (two * pi * n / (length - one)).cos()
            + a_two * (four * pi * n / (length - one)).cos()
            - a_three * (six * pi * n / (length - one)).cos()
    }
}

/// A rectangular window: <https://en.wikipedia.org/wiki/Window_function#Rectangular_window>
pub struct RectangularWindow;
impl<T> WindowFunction<T> for RectangularWindow
where
    T: RealNumber,
{
    fn is_symmetric(&self) -> bool {
        true
    }

    fn window(&self, _n: usize, _length: usize) -> T {
        let one = T::one();
        one
    }
}

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

    fn window_test<T, W>(window: W, expected: &[T])
    where
        T: RealNumber + Debug,
        W: WindowFunction<T>,
    {
        let mut result = vec![T::zero(); expected.len()];
        for i in 0..result.len() {
            result[i] = window.window(i, result.len());
        }

        for i in 0..result.len() {
            if (result[i] - expected[i]).abs() > T::from(1e-4).unwrap() {
                panic!("assertion failed: {:?} != {:?}", result, expected);
            }
        }
    }

    #[test]
    fn triangular_window32_test() {
        let window = TriangularWindow;
        let expected = [0.2, 0.6, 1.0, 0.6, 0.2];
        window_test(window, &expected);
    }

    #[test]
    fn hamming_window32_test() {
        let hamming = HammingWindow::<f32>::default();
        let expected = [0.08, 0.54, 1.0, 0.54, 0.08];
        window_test(hamming, &expected);
    }

    #[test]
    fn blackmanharris_window32_test() {
        let blackmanharris = BlackmanHarrisWindow;
        let expected = [0.0001, 0.2175, 1.0000, 0.2175, 0.0001];
        window_test(blackmanharris, &expected);
    }

    #[test]
    fn rectangular_window32_test() {
        let rectangular = RectangularWindow;
        let expected = [1.0, 1.0, 1.0, 1.0, 1.0];
        window_test(rectangular, &expected);
    }
}