Which of the following statements correctly describes the input-output relationship of a Schmitt trigger?

The statement that the output changes state at defined input thresholds accurately describes the behavior of a Schmitt trigger. A Schmitt trigger is a type of comparator circuit that introduces hysteresis into its operation. This means that it has different threshold levels for when the output will switch from a low state to a high state and vice versa.

As the input voltage crosses these well-defined thresholds, the Schmitt trigger output flips accordingly, creating a clean transition between the two output states. This transition helps to eliminate noise and provides a stable output that is particularly useful in digital circuits where precise switching is required.

In contrast, the other statements do not accurately reflect the function of a Schmitt trigger. The output does not directly follow the input, as it only changes states at specific thresholds rather than mirroring the input signal. The output is not linear with respect to the input; instead, it exhibits a distinct on/off digital behavior. Lastly, the output does not operate independently of the input; it is fundamentally dependent on it, but only within the framework of turning on or off at those defined thresholds.