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What does the Laplace transform really tell us?
The purpose of the Laplace Transform is to transform ordinary differential equations (ODEs) into algebraic equations, which makes it easier to solve ODEs. The Laplace Transform is a generalized Fourier Transform, since it allows one to obtain transforms of functions that have no Fourier Transforms.
What is Laplace transform in simple terms?
The Laplace transform is a way to turn functions into other functions in order to do certain calculations more easily. Functions usually take a variable (say t) as an input, and give some output (say f). The Laplace transform converts these functions to take some other input (s) and give some other output (F).
What is Laplace transform and its application?
(complex frequency). The transform has many applications in science and engineering because it is a tool for solving differential equations. In particular, it transforms linear differential equations into algebraic equations and convolution into multiplication.
Are Laplace transforms easy?
We will also see that, for some of the more complicated nonhomogeneous differential equations from the last chapter, Laplace transforms are actually easier on those problems as well.
Which is a physical interpretation of the Laplace transform?
This is a “physical” interpretation of the Laplace transform as the “present value” of a revenue stream, as a function of the interest rate. Is that pretty much the whole story of how to “physically” interpret the Laplace transform, or can more be said?
How are Laplace transforms used in infinite dimensional cases?
It should be noted that unlike in the finite case, in the infinite dimensional case care must be taken to ensure that the transform actually converges, but that is another problem entirely. Refer http://www.dspguide.com/CH32.PDF for an excellent explanation of Laplace Transforms in the Electrical Domain.
Is the kernel unitary in a Laplace transform?
For Fourier transforms the kernel is unitary, and while not true of Laplace transforms, the idea of it being a change of basis still holds. It should be noted that unlike in the finite case, in the infinite dimensional case care must be taken to ensure that the transform actually converges, but that is another problem entirely.
What are poles and zeros in Laplace transform?
The Laplace transform can be viewed as probing the system’s impulse response with various exponentially decaying sinusoids. Probing waveforms that produce a cancellation are called poles and zeros.