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Sure! The definition of Laplace transform involves the integral of a function, which always makes discontinuous continuous.

Q: Can a discontinuous function have a laplace transform?

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Fourier transform and Laplace transform are similar. Laplace transforms map a function to a new function on the complex plane, while Fourier maps a function to a new function on the real line. You can view Fourier as the Laplace transform on the circle, that is |z|=1. z transform is the discrete version of Laplace transform.

a pulse (dirac's delta).

find Laplace transform? f(t)=sin3t

They are similar. In many problems, both methods can be used. You can view Fourier transform is the Laplace transform on the circle, that is |z|=1. When you do Fourier transform, you don't need to worry about the convergence region. However, you need to find the convergence region for each Laplace transform. The discrete version of Fourier transform is discrete Fourier transform, and the discrete version of Laplace transform is Z-transform.

The type of response given by Laplace transform analysis is the frequency response.

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Fourier transform and Laplace transform are similar. Laplace transforms map a function to a new function on the complex plane, while Fourier maps a function to a new function on the real line. You can view Fourier as the Laplace transform on the circle, that is |z|=1. z transform is the discrete version of Laplace transform.

The Laplace transform is related to the Fourier transform, but whereas the Fourier transform expresses a function or signal as a series of modes ofvibration (frequencies), the Laplace transform resolves a function into its moments. Like the Fourier transform, the Laplace transform is used for solving differential and integral equations.

s

There are continuous functions, for example f(t) = e^{t^2}, for which the integral defining the Laplace transform does not converge for any value of the Laplace variable s. So you could say that this continuous function does not have a Laplace transform.

2/s

The Laplace transform of the unit doublet function is 1.

a pulse (dirac's delta).

Laplace will only generate an exact answer if initial conditions are provided

find Laplace transform? f(t)=sin3t

They are similar. In many problems, both methods can be used. You can view Fourier transform is the Laplace transform on the circle, that is |z|=1. When you do Fourier transform, you don't need to worry about the convergence region. However, you need to find the convergence region for each Laplace transform. The discrete version of Fourier transform is discrete Fourier transform, and the discrete version of Laplace transform is Z-transform.

The type of response given by Laplace transform analysis is the frequency response.

the most convenient solution is to use the laplace transform, connecting it in series makes a current loop in kvl, where the summation of e (the supply) equals the voltage in resistor, inductor and capaitor,, using differential ang integral, we can create a formula of function... to simplify use the laplace transform, then inverse laplace transform... after the action completed, you will now have a pronounced equation for current as a function of time