In the previous tweet, we talked about the physical meaning and the convergence domain of Lagrange transform. So what's the difference and connection between unilateral Laplace transform and bilateral Laplace transform?
Although we said earlier, “If there is no special explanation, we only consider the Lagrangian transformation of the causal signal (that is, the unilateral Laplace transformation), but we still need to find out the similarities and differences between the unilateral Laplace transform and the bilateral Laplace transform.
1, different in nature
Both unilateral Lapp transformation and bilateral Lapp transformation are more or less obvious or concealed in the following properties.
2, the application of different
A unilateral Laplace transformation can be used to solve a full response describing a differential equation, but only if the system is a causal system. There are examples of teaching materials in this area, so I will not repeat them here.
Let's look at a topic that can be solved with a unilateral Laplace transformation or a bilateral Laplace transformation. The results of the same solution and different processes are very intuitive and reflect the difference of unilateral and bilateral Laplace transforms.
This question is taken from Zheng Junli's "Signals and Systems, Third Edition", Volume 4-28
Solution: Method One, Using Unilateral Laplace Transform
The effect of the DC power supply E added at t<0 is converted into the initial energy storage of the system, which is solved using a unilateral Laplace transformation.
According to the meaning of the question, vc(0-)=E, when drawing t>0, the circuit diagram of s domain is shown in the following figure.
Method two, using bilateral Lapp transformation
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