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use std::cmp::{PartialOrd};
use ::num_traits::{Trig, Pow, ArithmeticOps, FractionOps};
use ::complex::Complex;
/// A data structure representing a sinusoid. AKA the sin or cos functions.
///
/// The general formula for a sinusoid is A cos(2πf + θ)
///
/// The number type is generic, but realistically it's only useful for
/// floats.
#[derive(Debug, Clone, PartialEq)]
pub struct Sinusoid<T> {
amplitude: T,
frequency: T,
phase: T
}
impl<T> Sinusoid<T> {
pub fn new(amplitude:T, frequency: T, phase: T) -> Sinusoid<T> {
Sinusoid {
amplitude: amplitude,
frequency: frequency,
phase: phase
}
}
}
impl<T> Sinusoid<T> where T: FractionOps + Copy {
/// The period is the time taken for each repetition of the
/// sinusoid
///
/// ```
/// use worthe_signals::sinusoid::Sinusoid;
/// use std::f32;
///
/// let sinusoid = Sinusoid::new(1.0 as f32, 0.5, 0.0);
/// assert!((sinusoid.period()-2.0).abs() < f32::EPSILON);
/// ```
pub fn period(&self) -> T {
self.frequency.recip()
}
}
#[derive(Debug, PartialEq)]
pub enum AddSinusoidError {
DifferentFrequency
}
impl<T> Sinusoid<T> where T: Trig + Pow + ArithmeticOps + Copy {
/// Converts the sinusoid to phasor form
///
/// This discards the frequency. Take care to only compare phasors
/// that had the same frequency before their conversion.
///
/// ```
/// use worthe_signals::sinusoid::Sinusoid;
/// use worthe_signals::complex::Complex;
/// use std::f32;
/// let pure_real = Sinusoid::new(1.0 as f32, 0.5, 0.0);
/// let pure_real_phasor = pure_real.to_phasor();
/// assert!((pure_real_phasor.real - 1.0).abs() < f32::EPSILON);
/// assert!((pure_real_phasor.imag - 0.0).abs() < f32::EPSILON);
///
/// let pure_imag = Sinusoid::new(1.0 as f32, 2.0, -f32::consts::FRAC_PI_2);
/// let pure_imag_phasor = pure_imag.to_phasor();
/// assert!((pure_imag_phasor.real - 0.0).abs() < f32::EPSILON);
/// assert!((pure_imag_phasor.imag + 1.0).abs() < f32::EPSILON);
/// ```
pub fn to_phasor(self) -> Complex<T> {
Complex::from_polar(self.amplitude, self.phase)
}
}
impl<T> Sinusoid<T> where T: Trig + Pow + ArithmeticOps + PartialEq + Copy {
/// Adds two sinusoids together into one sinusoid.
///
/// # Errors
///
/// This can only be done if the two sinusoids have the same
/// frequency.
///
/// ```
/// use worthe_signals::sinusoid::{Sinusoid, AddSinusoidError};
///
/// let sin1 = Sinusoid::new(1.0 as f32, 0.5, 0.0);
/// let sin2 = Sinusoid::new(1.0 as f32, 2.0, 0.0);
/// assert_eq!(Err(AddSinusoidError::DifferentFrequency), sin1.add(sin2));
/// ```
///
/// # Examples
///
/// ```
/// use worthe_signals::sinusoid::{Sinusoid, AddSinusoidError};
/// use std::f32;
///
/// let sin1 = Sinusoid::new(-3.0 as f32, 1.0, 0.0);
/// let sin2 = Sinusoid::new(4.0 as f32, 1.0, -f32::consts::FRAC_PI_2);
/// assert_eq!(Ok(Sinusoid::new(5.0, 1.0, -2.21429743558818100603413092035707408014009529080286529335)), sin1.add(sin2));
/// ```
pub fn add(self, other: Sinusoid<T>) -> Result<Self, AddSinusoidError> {
if self.frequency != other.frequency {
Err(AddSinusoidError::DifferentFrequency)
}
else {
let frequency = self.frequency;
let self_phasor = self.to_phasor();
let other_phasor = other.to_phasor();
let combined = self_phasor + other_phasor;
let (amplitude, phase) = combined.to_polar();
Ok(Sinusoid::new(amplitude, frequency, phase))
}
}
}
impl<T> Sinusoid<T> where T: FractionOps + ArithmeticOps + Trig + Copy {
/// Frequency can be considered in terms of the signal's number of
/// repetitions per second (referred to just as the frequency), or
/// the frequency in radians.
/// ```
/// use worthe_signals::sinusoid::Sinusoid;
/// use std::f32;
///
/// let sinusoid = Sinusoid::new(1.0 as f32, 1.0, 0.0);
/// assert!((sinusoid.radial_frequency()-2.0*f32::consts::PI) < f32::EPSILON);
/// ```
pub fn radial_frequency(&self) -> T {
T::two_pi()*self.frequency
}
/// A sinusoid can be sampled to get its value at a given point in
/// time.
///
/// ```
/// use worthe_signals::sinusoid::Sinusoid;
/// use std::f32;
///
/// let sinusoid = Sinusoid::new(1.0 as f32, 1.0, -f32::consts::FRAC_PI_2); //AKA sin
/// assert!((sinusoid.sample(0.0)-0.0).abs() < f32::EPSILON);
/// assert!((sinusoid.sample(0.25)-1.0).abs() < f32::EPSILON);
/// assert!((sinusoid.sample(0.5)-0.0).abs() < f32::EPSILON);
/// assert!((sinusoid.sample(0.75)+1.0).abs() < f32::EPSILON);
/// assert!((sinusoid.sample(1.0)-0.0).abs() < f32::EPSILON);
/// ```
pub fn sample(&self, t: T) -> T {
(self.radial_frequency()*(t%self.period()) + self.phase).cos() * self.amplitude
}
}
impl<T> Sinusoid<T> where T: FractionOps + ArithmeticOps + From<u16> + Trig + Copy + PartialOrd {
/// Sometimes, it's useful to sample at all of the points in a range
///
/// Start value is inclusive. End value is exclusive.
///
/// ```
/// use worthe_signals::sinusoid::Sinusoid;
/// use std::f32;
///
/// let sinusoid = Sinusoid::new(1.0 as f32, 1.0, -f32::consts::FRAC_PI_2); //AKA sin
/// let samples = sinusoid.sample_range(0.0, 100.0, 4.0);
/// assert_eq!(samples.len(), 400);
/// for i in (0..100).map(|i| i*4) {
/// assert!((samples[i+0]-0.0).abs() < f32::EPSILON, "Sample {} was {}", i+0, samples[i+0]);
/// assert!((samples[i+1]-1.0).abs() < f32::EPSILON, "Sample {} was {}", i+1, samples[i+1]);
/// assert!((samples[i+2]-0.0).abs() < f32::EPSILON, "Sample {} was {}", i+2, samples[i+2]);
/// assert!((samples[i+3]+1.0).abs() < f32::EPSILON, "Sample {} was {}", i+3, samples[i+3]);
/// }
/// ```
pub fn sample_range(&self, start: T, end: T, sample_rate: T) -> Vec<T> {
let mut result = Vec::new();
let mut i: u16 = 0;
loop {
let t = start + T::from(i)/sample_rate;
if t >= end {
break;
}
result.push(self.sample(t));
i += 1;
}
result
}
}
/*
#[cfg(test)]
mod tests {
use super::*;
use std::f32;
}
*/
|
