Questions tagged [minimum-phase]

Problem statement I have a collection of magnitude (only) responses I'd like to turn into FIR filter kernels that are matched in phase "minimal" in phase, with respect to the complete system have little to no "pre-ring" maintain the design…

Consider a dynamic system $$\dot{x}=Ax+Bu \text{ and } y=Cx$$ The transfer function is $$sX(s) = AX(s)+BU(s),$$ so $$(sI-A)X(s)=BU(s)$$ and $$Y(s)=CX(s)$$ combining the two transfer equations, we have $$Y(s)=C(sI-A)^{-1}BU(s),$$ so…

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?