Howtosignalprocessing
- How do you know if a system is causal or stable?
- What does the Laplace transform really tell us?
- What are the conditions for existence of Laplace transformation?
- How many theorems are there in Laplace transform?
How do you know if a system is causal or stable?
Hence, the system is causal. A system is said to invertible if the input of the system appears at the output. The system is said to be stable only when the output is bounded for bounded input. For a bounded input, if the output is unbounded in the system then it is said to be unstable.
What does the Laplace transform really tell us?
The Laplace transform is used to solve differential equations. It is accepted widely in many fields. We know that the Laplace transform simplifies a given LDE (linear differential equation) to an algebraic equation, which can later be solved using the standard algebraic identities.
What are the conditions for existence of Laplace transformation?
Note: A function f(t) has a Laplace transform, if it is of exponential order. Theorem (existence theorem) If f(t) is a piecewise continuous function on the interval [0, ∞) and is of exponential order α for t ≥ 0, then Lf(t) exists for s > α.
How many theorems are there in Laplace transform?
There are two results/theorems establishing connections between shifts and exponential factors of a function and its Laplace transform.
