## Pages

### Z transform stability

In Z transform in DSP that is a necessary and sufficient condition for the system to be BIBO stable is given as below. This article gives information about Z transform stability to better understand this topic.

n=∞
∑   |h(n)| <  ∞
n=-∞

n=∞
H(Z) = ∑   h(n)  z-n
n=-∞

n=∞
|H(Z)| =| ∑   h(n)  z-n |
n=-∞

The magnitude of the overall sum is less than the sum of the magnitude of individual terms

n=∞
|H(Z)| < ∑   |h(n)|  | z-n |
n=-∞

If H(z) is evaluated on the unit circle, then | z-n | = 1

n=∞
|H(Z)| < ∑   |h(n)|
n=-∞

If the system is BIBO stable, then

n=∞
∑   |h(n)|   < ∞
n=-∞

|H(z)| < ∞

This condition requires that the unit circle should be present in the ROC full form of H(Z).
In Z transform in DSP that is a necessary and sufficient condition for the system to be BIBO stable is given as below. This article gives information about Z transform stability to better understand this topic.

n=∞
∑   |h(n)| <  ∞
n=-∞

n=∞
H(Z) = ∑   h(n)  z-n
n=-∞

n=∞
|H(Z)| =| ∑   h(n)  z-n |
n=-∞

The magnitude of the overall sum is less than the sum of the magnitude of individual terms

n=∞
|H(Z)| < ∑   |h(n)|  | z-n |
n=-∞

If H(z) is evaluated on the unit circle, then | z-n | = 1

n=∞
|H(Z)| < ∑   |h(n)|
n=-∞

If the system is BIBO stable, then

n=∞
∑   |h(n)|   < ∞
n=-∞

|H(z)| < ∞

This condition requires that the unit circle should be present in the ROC full form of H(Z).