In signals & systems, control theory, we use laplace for LTI etc..What is the distinction instead of Fourier transform?

Laplace change is in the facility domain (s=R*jw) while Fourier transform is in jw plane. In basic words, Fourier transform is the special case of Laplace transform.

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1. Fourier change is the special case of laplace change which is evaluated maintaining the real component zero.
2. Fourier change is typically used for analysis in frequency domain vice versa, laplace transform is typically used for analysis in s-domain(it's no frequency domain).
3. Fourier change helps us to examine anything in the frequency domain vice versa, laplace change is commonly done for facility analysis (when anything is not easier to analyse with time domain, we transform it right into s domain and then take it the inverse laplace change to complete the analysis). Laplace transform is generally used for mechanism Analysis,where together Fourier change is provided for Signal Analysis.

IN situation of laplace transform you require to have actually real role where together in instance of fourier transform you can have complicated as well together real duty moreover in instance of fourier change you can control the border of integration
IN case of laplace change you require to have actually real role where as in case of fourier change you deserve to have facility as well together real function moreover in situation of fourier change you can manage the limit of integration
If we placed the exp(-sigma t) to multiply the Fourier transform, then it becomes the Laplace transform. We can conveniently see that what is created in the Fourier transform as exp(-jwt), now becomes exp(-st) whereby s = sigma + jw. The sigma is the real or referred to as as the exponential part, wherein the jw is the imagine or called sinusoidal part. The Fourier change does no really care on the changing magnitudes that a signal, whereas the Laplace change 'care' both the transforming magnitudes (exponential) and also the oscillation (sinusoidal) parts. We can say the Fourier transform is a subset the Laplace transform.
The Laplace change is essentially valuable for solving differential equations, due to the fact that most of any kind of differential equation's equipment will save on computer exponential and also sinusoidal parts. The solution deserve to be more easily express and understand in the s domain.
Laplace change transforms a signal to a complicated plane s. Fourier change transforms the exact same signal right into the jw plane and is a special situation of Laplace transform where the real component is 0. In Laplace domain, s=r+jw wherein r is the real part and the imaginary part depicts the oscillatory component.
1. Fourier transform is the special situation of laplace change which is evaluated maintaining the real part zero.
2. Fourier change is generally used for analysis in frequency domain whereas laplace change is typically used for evaluation in s-domain(it's not frequency domain).
3. Fourier change helps united state to examine anything in the frequency domain vice versa, laplace transform is typically done for complex analysis (when anything is not simpler to analyse over time domain, we transform it into s domain and then take it the station laplace change to complete the analysis).
The La place transform is a device to resolve the straight differential equation in an easy and elegant way since that transforms a linear differential equation right into algebraic equation.
In stimulate to solve for the solution of a mechanism in a time domain top top an applications of time domain stimuli, one need to solve the direct system that the differential equations mathematically modelling the system along with the initial and also boundary conditions. Such equipment will be usually tedious.
But making use of the La place transform to transform the equations indigenous time domain right into the S-domain, i m sorry is called the facility frequency domain, one can transform the time domain differential equations into S-domain algebraic equations.
Naturally simultaneously solving algebraic equations is much easier than addressing simultaneous differential equations. This is the strength of this math transformation.
As because that the Fourier transform, that is a tool for transforming time domain attributes into frequency domain function. Physically any type of time domain duty can be assumed of a summation of complex exponential signals. And this what the Fourier transform yield. So, the is an evaluation tool the time domain signals.
Laplace transform is simply a generalization that Fourier Transform. If you notification computing Laplace transform is simpler that Fourier, however, the station Laplace change is lot harder come compute compared to Fourier inverse transform since the integrals are over facility limits.
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