Signals in Natural Domain
Chapter 3 :  Discrete-Time Systems
 
Stability :
There are several definitions for stability. Here we will consider bounded input bonded output (BIBO) stability. A system is said to be BIBO stable if every bounded input produces a bounded output. We say that a signal {x[n]} is bounded if
|x[n]| < M < ∞    for all  n

The moving average system
$\displaystyle y[n]=\frac{1}{2N+1}\sum\limits_{k=-N}^{N}x[n]$

is stable as y[n] is sum of finite numbers and so it is bounded. The accumulator system defined by
$\displaystyle y[n]=\sum\limits_{k=- \infty}^{n}x[k]$

is unstable. If we take {x[n]} = {u[n]}, the unit step then y[0] = 1, y[1] = 2, y[2] = 3,    are y[n] = n +1, n ≥ 0 so y[n]grows without bound.
 
 
 
 
 
 
 
 
 
 
 
 
 
 
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