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Thread: complex signal

  1. #1
    Join Date
    Jan 2022
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    complex signal

    hello i would like to ask how to generate the complex signal f(t)=exp^(j*omega*t), j=sqrt(-1), in C++. thanks very much

  2. #2
    Join Date
    Feb 2017
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    Re: complex signal

    Quote Originally Posted by sddfds View Post
    hello i would like to ask how to generate the complex signal f(t)=exp^(j*omega*t), j=sqrt(-1), in C++. thanks very much
    C++ has a standard library to handle complex numbers,

    https://en.cppreference.com/w/cpp/numeric/complex

    Say you have,

    f(t) = exp^(j*omega*t)

    Note that the imaginary unit j plays a role in formula manipulations only. It is never calculated as sqrt(-1). This is because that number does not exist for real. It is imaginary. So in numeric calculations, a complex number is represented by a tuple of two real numbers, meaning a + j*b is represented by (a,b). Using (a.b) notation the f(t) formula becomes,

    f(t) = exp^((0, omega*t))

    Now, according to Euler's formula,

    https://en.wikipedia.org/wiki/Euler%27s_formula

    the result of the f(t) formula should equal the complex number (cos(omega*t), sin(omega*t)). That is, this equality is supposed to hold,

    (cos(omega*t), sin(omega*t)) == exp^((0, omega*t))

    The omega*t number will be interpreted as an angle by the sin and cos functions. Let us set it to 135 degrees (3*PI/4 radians) and check it out in a C++ program,

    Code:
    #include <numbers>
    #include <complex>
    #include <iostream>
    
    void test() {
    
    	using Complex = std::complex<double>;
    
    	const double PI = std::numbers::pi; // since C++ 20
    	const double angle_135 = 3.0*PI/4.0; 
    
    	Complex f = std::exp(Complex(0.0, angle_135));
    
    	std::cout << f << std::endl;
    	std::cout << std::cos(angle_135) << "," << std::sin(angle_135) << std::endl;
    }
    The result becomes (-0.707107, 0707107) in both cases as the Euler formula predicts. Both ways will give you f(t).
    Last edited by wolle; January 9th, 2022 at 02:37 AM.

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