In a car, does matching the EQ of both the left and right side using IIRfilters mean that I'm matching the phase of each side? I have someone telling me that the car's environment is mostly minimum phase and that matching the left and right side will match its phase response. I have never heard of such a thing. I know they would match amplitude but would highly doubt they're matching the phase which is something an FIR filter would actually do. Any help would be appreciated.
Two minimum phase IIR filters with different magnitude responses generally will have different phase responses. But two minimum phase IIR filters with exactly same magnitude responses will exactly have same phase responses. (How can two systems with exactly same transfer functions have different magnitude/phase responses?). If the first filter is a minimum phase filter and the second filter has exactly same magnitude response but different phase response then the second filter is not minimum phase.
In contrary, two linear phase FIR filters with different magnitude responses may have exactly same phase responses when the required conditions are fulfilled. (E.g same delays, same symmetric types, and no negation).