basic_dsp 0.2.1

Digital signal processing based on 1xN (one times N) or Nx1 vectors in real or complex number space. Vectors come with basic arithmetic, convolution, Fourier transformation and interpolation operations.
Documentation 
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use num::complex::Complex;
use num::traits::Float;
use std::{f32,f64};

pub trait ComplexExtensions<T>
    where T: Float
{
    fn cos(&self) -> Self;
    fn sin(&self) -> Self;
    fn sqrt(&self) -> Self;
    fn powf(&self, value: T) -> Self;
    fn ln(&self) -> Self;
    fn expn(&self) -> Self;
    fn log_base(&self, value: T) -> Self;
    fn exp_base(&self, value: T) -> Self;
}

macro_rules! add_complex_extensions {
    ($($data_type:ident);*)
	 =>
	 {	 
        $(
            impl ComplexExtensions<$data_type> for Complex<$data_type>
            {   
                fn sin(&self) -> Self {
                    let re = self.re;
                    let im = self.im;
                    Complex::new(
                        re.sin() * im.cosh(), 
                        re.cos() * im.sinh())
                }
                
                fn cos(&self) -> Self {
                    let re = self.re;
                    let im = self.im;
                    Complex::new(
                        re.cos() * im.cosh(), 
                        -re.sin() * im.sinh())
                }
                   
                fn sqrt(&self) -> Self {
                    let (r, theta) = self.to_polar();
                    Complex::from_polar(&(r.sqrt()), &(theta/2.0))
                }
                
                fn powf(&self, value: $data_type) -> Self {
                    let (r, theta) = self.to_polar();
                    Complex::from_polar(&(r.powf(value)), &(theta*value))
                }
                
                fn ln(&self) -> Self {
                    let (r, theta) = self.to_polar();
                    Complex::new(r.ln(), theta)
                }
                
                fn expn(&self) -> Self {
                    let re = self.re;
                    let im = self.im;
                    let exp = re.exp();
                    // Equation is taken from http://mathfaculty.fullerton.edu/mathews/c2003/ComplexFunExponentialMod.html
                    Complex::new(exp * im.cos(), exp * im.sin())
                }
                
                fn log_base(&self, value: $data_type) -> Self {
                    let (r, theta) = self.to_polar();
                    let e = $data_type::consts::E;
                    Complex::new(r.log(value), theta * e.log(value))
                }
                
                // Same as value.powf(self) but I would prefer to have this version
                // around too
                fn exp_base(&self, value: $data_type) -> Self {
                    let ln = value.ln();
                    let exp = (self.re * ln).exp();
                    let im = self.im * ln; 
                    Complex::new(exp * im.cos(), exp * im.sin())
                }
            }
        )*
     }
}
add_complex_extensions!(f32; f64);

#[cfg(test)]
mod tests {
	use super::*;
	use num::complex::Complex32;
    
    fn assert_complex(left: Complex32, right: Complex32) {
        assert!((left.re - right.re).abs() < 1e-4);
        assert!((left.im - right.im).abs() < 1e-4);
    }
	
    #[test]
	fn powf_test()
	{
		let c = Complex32::new(2.0, -1.0);
        let r = c.powf(3.5);
        assert_complex(r, Complex32::new(-0.8684746, -16.695934));
	}
    
    #[test]
	fn logn_test()
	{
		let c = Complex32::new(2.0, -1.0);
        let r = c.ln();
        assert_complex(r, Complex32::new(0.804719, -0.4636476));
	}
    
    #[test]
	fn expn_test()
	{
		let c = Complex32::new(2.0, -1.0);
        let r = c.expn();
        assert_complex(r, Complex32::new(3.9923239, -6.217676));
	}
    
    #[test]
	fn log_test()
	{
		let c = Complex32::new(2.0, -1.0);
        let r = c.log_base(10.0);
        assert_complex(r, Complex32::new(0.349485, -0.20135958));
	}
    
    #[test]
	fn exp_test()
	{
		let c = Complex32::new(2.0, -1.0);
        let r = c.exp_base(10.0);
        assert_complex(r, Complex32::new(-66.82015, -74.39803));
	}
}