Not that the fact is true "if and only if"

**Part 1**

Sufficiency: If

Use convolution formula

**Part 2:**

*Necessity*: If
*not* BIBO.

#### Note:

#### Note:

*sign*of time-reversed

#### Note:

*not* BIBO.

Summary: An overview of BIBO stability.

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With finite length signals

But this can happen with

- Definition 1: Bounded-Input Bounded-Output (BIBO) Stable
- When, in an LSI system, for any bounded input the output is always bounded.

An LSI system is BIBO stable if and
only if the impulse response
h ∈
l
1
Z
h
l
1
.

Not that the fact is true "if and only if"

Sufficiency: If

Use convolution formula

*Necessity*: If
*not* BIBO.

This part is tricky!!!

We only have 1
x
x to show this.

*not* BIBO.

Need:

Is it BIBO stable?

Is it BIBO stable?