definition of input/output resistance of a circuit
For defining or calculating the input impedance you have to discriminate berween DC and AC.
For DC signals you can define the voltage-to-current ratio for small as well as also for large signals (where the voltage-to-current relation is non-linear).

However, for AC signals the input impedance is defined for small signals only because a voltage-to-current ratio can be meaningful defined for identical (sinusoidal) waveforms only. Because linearity is not ensured for "large signal operation" the term "impedance" applies to small-signal operation only.