Laplace Transform?

Question

What is the practical application of Laplace Transform and Fourier Series in communication systems and Electronics, why we use it, is there any alternative.

Answer 1

Would you rather solve a differential equation, or a (much simpler) algebraic equation? That's what the Laplace transform (and other similar transforms, like the Z-transform) do for you.

Networks of resistors, capacitors, inductors and semiconductor devices (modeled as resistors, capacitors, inductors) have transfer functions that are given by differential equations. Laplace transforms 'transform' those into simpler algebraic equations, which are easier to solve. Once you have the solution, you take the inverse Laplace transform to move back to the time domain.

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Answer 2

They take signals that are very complex in the time domain ... e.g. modulated radio signal and express them very simply in the frequancy domain. You can then apply filtering, amplification or mixing algorithms with simple arithmetic and then transform them back to the time domain to get the result without using hairy math.