Under BIBO stability, if the input is bounded, what can be said about the output?

Under BIBO stability, if the input is bounded, what can be said about the output?

• A. It remains bounded.
• B. It becomes unbounded.
• C. It is always periodic.
• D. It is identically zero.

Answer: (A)

Under BIBO stability, a bounded input produces a bounded output. This means if the input stays within some finite amplitude, the system’s response stays within a finite envelope as well. For an LTI system, the bound on the output is proportional to the input bound, with the proportionality given by the system’s impulse response (specifically, the L1 norm of that impulse response). So the output remains bounded, though it need not be zero or periodic; it simply stays within a finite range determined by the system.