Unit Impulse Bounded or Unbounded?

Yes, the unit impulse "height" is unbounded, but the "strength" of the signal as the way it is mentioned in many texts, is finite, given by the area of the unit impulse.

1. Is unit step bounded or unbounded?
2. Is impulse function BIBO stable?
3. What is bounded and unbounded signals?
4. What is the integral of unit impulse?

Is unit step bounded or unbounded?

It's true that the unit step function is bounded. However, a system which has the unit step function as its impulse response is not stable, because the integral (of the absolute value) is infinite.

Is impulse function BIBO stable?

The impulse response is not absolutely integrable, hence the system is not BIBO stable. From the corresponding transfer function H(s)=1/s, you can see that there is a single pole at the origin. Systems with single poles on the imaginary axis, like the integrator in your example, are also called marginally stable.

What is bounded and unbounded signals?

A continuous-time signal x(t) having finite value at any instant of time is said to be bounded signal i.e. if x(t) < M ; where M is the finite value for all time t. The bounded signal example with M=1 shown in Figure 1.

What is the integral of unit impulse?

The unit impulse function has zero width, infinite height and an integral (area) of one. We plot it as an arrow with the height of the arrow showing the area of the impulse.