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How can I find the total harmonic distortion of a nonlinear signal. Using matlab

How can I find the total harmonic distortion of a nonlinear signal. For example, Forced Van der pol Oscillator with code as shown below. I have tried the 'thd' function in matlab but I guess I'm missing somethings. This is the equation x''-mu(1-x^2(t))x'(t)+x(t)=Pcos(w*t)

function vdpo()
t=0:0.001:10
mu=2
x0=-2;
v0=2;
p=10; w=7;
 [t,x]= ode45(@f, t, [x0,v0])
function dxdt=f(t,x)
dxdt1=x(2); dxdt2= mu(1-x(1)^2)*x(1)+p*cos(w*t); 
dxdt=[dxdt1 ;dxdt2];
end
end
Solution

  • Try the code below, in which function f(t,x) is our ODE equations and we call function ode45 to use Runge-Kutta methods to solve it.

    function [x]=vdpo()
  t=0:0.001:10
  mu=2
  x0=-2;
  v0=2;
  p=10; w=7;
  [t,x]= ode45(@f, t, [x0,v0])
  function dxdt=f(t,x)
    dxdt1=-x(2)-x(1)+(x(1)^3)/3; dxdt2=-x(1)+p*cos(w*t); 
    dxdt=[dxdt1 ;dxdt2];
  end
end

    However, it is actually a math problem rather than a programming problem. The first thing that we have to do is to transform the equations into a more convenient form by defining y=x'+((x^3)/3-x)*mu, then we have 2 First Order Ordinary Differential Equations so we could call ode45 to solve it. I looked them through at here(page2).

    By calling 

    X=vdpo();
x=X(:,1);
thd(x)

    we could get an answer like: enter image description here

    p.s. NOT CERTAIN about THD part.