Anyone know of an approachable proof of the Caratheodory-Fejer theorem?

A colleague of mine recently lent a hand implementing a polynomial approximation routine I could port to our compiler, though it wasn&rsquo;t the method I was expecting. As I had written about previously, I was studying the Remez algorithm and implementing a prototype in Python. Remez approximation involves an iterated loop that alternates between root-finding and linear-system solving, and as…