Stability
The transfer function allows us to judge whether or not a system is bounded-input, bounded-output (BIBO) stable. To be specific, the BIBO stability criteria requires that the ROC of the system includes the unit circle. For example, for a causal system, all poles of the transfer function have to have an absolute value smaller than one. In other words, all poles must be located within a unit circle in the -plane.
The poles are defined as the values of which make the denominator of equal to 0:
Clearly, if then the poles are not located at the origin of the z-plane. This is in contrast to the FIR filter where all poles are located at the origin, and is therefore always stable.
IIR filters are sometimes preferred over FIR filters because an IIR filter can achieve a much sharper transition region roll-off than FIR filter of the same order.
Read more about this topic: Infinite Impulse Response
Famous quotes containing the word stability:
“Every nation ... whose affairs betray a want of wisdom and stability may calculate on every loss which can be sustained from the more systematic policy of its wiser neighbors.”
—James Madison (1751–1836)
“The world can be at peace only if the world is stable, and there can be no stability where the will is in rebellion, where there is not tranquility of spirit and a sense of justice, of freedom, and of right.”
—Woodrow Wilson (1856–1924)
“...I feel anxious for the fate of our monarchy, or democracy, or whatever is to take place. I soon get lost in a labyrinth of perplexities; but, whatever occurs, may justice and righteousness be the stability of our times, and order arise out of confusion. Great difficulties may be surmounted by patience and perseverance.”
—Abigail Adams (1744–1818)