Is $\cos(x[n])$ stable? [closed]

1. Is Cos function stable?
2. Is cosine BIBO stable?
3. How do you know if an equation is BIBO stable?
4. Is the circuit BIBO stable?

Is Cos function stable?

If we provide a bounded input such as x[n]=u[n], the output is bounded. Now if we provide an unbounded signal x[n]=δ[n], the output oscillates between −1 and 1. So I think it's marginally stable in this case.

Is cosine BIBO stable?

Yes, system is BIBO stable. , which clearly depends on a future value of x(t) viz. x(1).

How do you know if an equation is BIBO stable?

A system is BIBO stable if and only if the impulse response goes to zero with time. If a system is AS then it is also BIBO stable (as the poles of the transfer function are a subset of the poles of the system).

Is the circuit BIBO stable?

Basically, a system is BIBO stable if and only if nice inputs produce nice outputs.