Time Setting of $z$ and Laplace Transforms

1. What is the relation between Laplace transform and z-transform?
2. What is time scaling in Laplace transform?
3. What is time shifting property of Laplace transform?
4. Why is z 1 delay?

What is the relation between Laplace transform and z-transform?

The Laplace Transform also overcomes some of the convergence problems associated with the continuous-time Fourier Transform, and can handle a broader class of signal waveforms. The z-transform, on the other hand, is especially suitable for dealing with discrete signals and systems.

What is time scaling in Laplace transform?

Time Scaling Property of Laplace Transform

Statement - The time scaling property of Laplace transform states that if, x(t)LT↔X(s) Then. x(at)LT↔1|a|X(sa) Proof.

What is time shifting property of Laplace transform?

Hence, it proves that a time shift of t₀ corresponds to the multiplication by a complex exponential e−st0 in the s-domain.

Why is z 1 delay?

polynomial by z-1 simply subtracts one from each exponent in the polynomial, thereby creating a delay of one.