Howtosignalprocessing
- How do you find the ROC of Laplace transform?
- Is it possible to find Laplace transform of every function?
- How do you find the region of convergence in Z-transform?
- How do you find the Laplace transform of a function?
How do you find the ROC of Laplace transform?
ROC of Left-Sided Signals
For a left-sided signal x(t), the ROC of the Laplace transform X(s) is Re(s)<σ2 where σ2 is a constant. Therefore, the ROC of the Laplace transform of a left-sided signal is to the left of the line σ=σ2.
Is it possible to find Laplace transform of every function?
It must also be noted that not all functions have a Laplace transform. For example, the function 1/t does not have a Laplace transform as the integral diverges for all s. Similarly, tant or et2do not have Laplace transforms.
How do you find the region of convergence in Z-transform?
For x(n)=δ(n), i.e., impulse sequence is the only sequence whose ROC of Z-transform is the entire z-plane. If x(n) is an infinite duration causal sequence, then its ROC is |z|>a, i.e., it is the exterior of a circle of the radius equal to a.
How do you find the Laplace transform of a function?
If you create a function by adding two functions, its Laplace Transform is simply the sum of the Laplace Transform of the two function. If you create a function by multiplying two functions in time, there is no easy way to find the Laplace Transform of the resulting function.
