What do input impedance and output impedance mean? What is the role of analyzing them?

Using Thevenin equivalence, the equivalent impedance of each element seen from the input end (open circuit) is called input impedance and analog output.

Electrical impedance is the general name of resistance, inductance and capacitance that hinder AC current in the circuit. The unit of impedance is ohm. Impedance measures the resistance of alternating current in a circuit. Impedance extends the concept of resistance to the field of AC circuit, which not only describes the relative amplitude of voltage and current, but also describes its relative phase. When the current through the circuit is DC, the resistance is equal to the impedance, and the resistance can be regarded as the impedance with zero phase. In vibration system, the impedance is also expressed by z, which is a complex number and a phasor, including amplitude and phase/polarity. It consists of resistance and reaction. Resistance is the consumption of energy, while reaction is the preservation of energy. In vibration system, the resistance produced by mass is mass resistance, and the resistance produced by stiffness is stiffness resistance.