Stability and Minimum-phase Property Preserved
A continuous-time causal filter is stable if the poles of its transfer function fall in the left half of the complex s-plane. A discrete-time causal filter is stable if the poles of its transfer function fall inside the unit circle in the complex z-plane. The bilinear transform maps the left half of the complex s-plane to the interior of the unit circle in the z-plane. Thus filters designed in the continuous-time domain that are stable are converted to filters in the discrete-time domain that preserve that stability.
Likewise, a continuous-time filter is minimum-phase if the zeros of its transfer function fall in the left half of the complex s-plane. A discrete-time filter is minimum-phase if the zeros of its transfer function fall inside the unit circle in the complex z-plane. Then the same mapping property assures that continuous-time filters that are minimum-phase are converted to discrete-time filters that preserve that property of being minimum-phase.
Read more about this topic: Bilinear Transform
Famous quotes containing the words stability, property and/or preserved:
“Traditions are the “always” in life—the rituals and customs that build common memories for children, offer comfort and stability in good times and bad, and create a sense of family identity.”
—Marian Edelman Borden (20th century)
“Things have their laws, as well as men; and things refuse to be trifled with. Property will be protected.”
—Ralph Waldo Emerson (1803–1882)
“The unity of effect or impression is a point of the greatest importance. It is clear, moreover, that this unity cannot be thoroughly preserved in productions whose perusal cannot be completed at one sitting.”
—Edgar Allan Poe (1809–1849)