Difference beteween fourier and laplace transform
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Ø Fourier is a subset of Laplace. Laplace is a more generalized transform.
Fourier is used primarily for steady state signal analysis, while Laplace is used for transient signal analysis. Laplace is good at looking for the response to pulses, step functions, delta functions, while Fourier is good for continuous signals.
Transforms are used because the time-domain mathematical models of systems are generally complex differential equations. Transforming these complex differential equations into simpler algebraic expressions makes them much easier to solve. Once the solution to the algebraic expression is found, the inverse transform will give you the time-domain repsponse.
For many years I have tried to obtain a good answer for the Laplace and Fourier transforms relationship. Many of the explanations just mention that the relationship is that s=a+jw, so the Fourier transform becomes a special case of the laplace transform. Sad explanation. Better explanations deals that Laplace is used for stability studies and Fourier is used for sinusoidal responses of systems. Using that information, I conclude that as systems are stable if the real part of s is negative, that is to say there is a transient that will vanish in time, in those cases, it is enaugh to use Fourier. Of course you will lose the insight of the transient part. Laplace should be able to determine the full response of a system, be it stable or unstable, including transient parts.
Fourier is used primarily for steady state signal analysis, while Laplace is used for transient signal analysis. Laplace is good at looking for the response to pulses, step functions, delta functions, while Fourier is good for continuous signals.
Transforms are used because the time-domain mathematical models of systems are generally complex differential equations. Transforming these complex differential equations into simpler algebraic expressions makes them much easier to solve. Once the solution to the algebraic expression is found, the inverse transform will give you the time-domain repsponse.
For many years I have tried to obtain a good answer for the Laplace and Fourier transforms relationship. Many of the explanations just mention that the relationship is that s=a+jw, so the Fourier transform becomes a special case of the laplace transform. Sad explanation. Better explanations deals that Laplace is used for stability studies and Fourier is used for sinusoidal responses of systems. Using that information, I conclude that as systems are stable if the real part of s is negative, that is to say there is a transient that will vanish in time, in those cases, it is enaugh to use Fourier. Of course you will lose the insight of the transient part. Laplace should be able to determine the full response of a system, be it stable or unstable, including transient parts.
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