Question

Please compare between the Fourier Transform and Laplace Transform.

Please solve by expert and make it clear to understand step by step and make your hand write

Answer 1

The solution to the above problem is given below. Please review the answer and let me know if you have any doubts.

Sol:- - The Continuous time fourier transform of a time domain function at is given by ). X(w) = f {w} = Swee just de And the 2-sided laplace transform is given by :- XLS) = {x147} = Battestat - fourier transform are for converting a time - Varing function into the frequency domain, whereas (aplace Converts a positive reel Variable t to a function of complex variable s. The main drawback of fourier transform is that it can be defined only for stable system, where as (aplace can be defined for both stable as well as unstable system. , Laplace transforms Can Capture the transient behaviors of Systems. fourier transforms only capture the steady state behavior. The Laplace transform is a generalized fourier transform, since it allows one to obtain transforms of functions that have no fourier transform,