title: Fit sine wave with a distorted time-base
body: <p>I want to know the best way to fit a sine-wave with a distorted time base, in Matlab.</p>
  
  <p>The distortion in time is given by a n-th order polynomial (n~10), of the form <code>t_distort = P(t)</code>.</p>
  
  <p>For example, consider the distortion <code>t_distort = 8 + 12t + 6t^2 + t^3</code> (which is just the power series expansion of <code>(t-2)^3</code>).</p>
  
  <p>This will distort a sine-wave as follows:</p>
  
  <p><a href="https://i.stack.imgur.com/4jRO3.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/4jRO3.png" alt="IMG"></a>
  </p>
  
  <p>I want to be able to find the distortion given this distorted sine-wave. (i.e. I want to find the function <code>t = G(t_distort)</code>, but <code>t_distort = P(t)</code> is unknown.)</p>