Validity of an argument that two transfer functions are minimum-phase based on their ratio being minimum-phase

1. What is minimum-phase maximum phase?
2. What is minimum-phase impulse response?
3. What is minimum-phase Hilbert transform?

What is minimum-phase maximum phase?

A causal stable LTI system E with transfer function H(z) with all zeros inside the unit circle is called minimum phase. A causal stable system E with transfer function H(z) with all zeros outside the unit circle is called maximum phase.

What is minimum-phase impulse response?

Minimum phase in the time domain

For all causal and stable systems that have the same magnitude response, the minimum phase system has its energy concentrated near the start of the impulse response. i.e., it minimizes the following function which we can think of as the delay of energy in the impulse response.

What is minimum-phase Hilbert transform?

the Hilbert transform of a constant is zero so the minimum-phase result will be unchanged no matter how G[k] is scaled.