I know in a minimum-phase system, any poles or zeros are reflected. How do I show that a minimum phase system is unique, or that only one system with that magnitude response can be minimum phased?
If you reflect any of the poles, the system becomes unstable (but even lower in phase before it blows up). If you reflect any of the zeros, the phase increases, so no other placement of zeros can be minimum. If the system response is a rational polynomial, then the factorization is unique, so no other (finite?) set of poles and zeros works the same (magnitude response).