Howtosignalprocessing
An improper system cannot be causal and stable. If the order of the numerator is greater than the order of the denominator, you'll always have at least one pole at infinity. Consequently, not all poles are in the left half-plane (or inside the unit circle in the case of discrete-time systems).
- Can a system be stable and causal?
- What is a system said to be causal and stable?
- How do you know if a system is causal?
- What does it mean for a transfer function to be proper?
Can a system be stable and causal?
The condition for both causality and stability can now be derived as follows. A causal system should have a region of convergence outside the outermost pole. A stable system should have the unit circle in its region of convergence. Therefore, a causal and stable system should have all poles inside the unit circle.
What is a system said to be causal and stable?
Concept: A causal system is a system where the output depends on past and current inputs but not future inputs. Ex: y(4) = x(√4) = x(2) , as output depends on past values of input. A system is said to be stable if every bounded input produces the bounded output.
How do you know if a system is causal?
A system is said to be causal if it does not respond before the input is applied. In other words, in a causal system, the output at any time depends only on the values of the input signal up to and including that time and does not depend on the future values of the input.
What does it mean for a transfer function to be proper?
A strictly proper transfer function is a transfer function where the degree of the numerator is less than the degree of the denominator. The difference between the degree of the denominator (number of poles) and degree of the numerator (number of zeros) is the relative degree of the transfer function.
