# Questions tagged [laplace-transform]

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### What is z equal to in z-transform?

In some places, it is said that z is equal to: $$z = e^s \quad where \quad s = \sigma + j \Omega$$ But in some places, it is said that z is equal to: $$z = e^{sT_s} \quad$$ where Ts is a sampling ...
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### Pole Magnitude and Damping Ratio relationship

I know that the damping ratio of a system is defined by the angle of the pole, calculated with respect to the left hand side $x$-axis. Could one infer though, that if the magnitude of the poles is ...
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### How can we prove the correctness of the integration property of the Laplace transform?

I was going through an Electrical Engineering textbook for understanding the Laplace transform and came across the following proof for one of the properties of the Unilateral Laplace transform. ...
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### RoC and Stability of a Rectangular Signal

If we have a system with an impulse defined as: $$h(t)=u(t)-u(t-2)$$ Then the Laplace Transform of h(t) would be the transfer function: $$H(s)=\frac{1}{s}-\frac{e^{-2s}}{s}, \quad Re(s)>0$$ We also ...
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### Names of system functions in frequency domain

I was just trying to refresh my systems theory known from long ago, and I realized that I had forgetten the name of the basic functions. Specifically, what are the names of these functions ...
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