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The Laplace transform is related to the Fourier transform, but whereas the Fourier transform expresses a function or signal as a series of modes ofvibration (frequencies), the Laplace transform resolves a function into its moments. Like the Fourier transform, the Laplace transform is used for solving differential and integral equations.

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Q: What is relation between laplace transform and fourier transform?
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What is the difference between a Fourier transform and a Laplace transform?

Laplace = analogue signal Fourier = digital signal Notes on comparisons between Fourier and Laplace transforms: The Laplace transform of a function is just like the Fourier transform of the same function, except for two things. The term in the exponential of a Laplace transform is a complex number instead of just an imaginary number and the lower limit of integration doesn't need to start at -∞. The exponential factor has the effect of forcing the signals to converge. That is why the Laplace transform can be applied to a broader class of signals than the Fourier transform, including exponentially growing signals. In a Fourier transform, both the signal in time domain and its spectrum in frequency domain are a one-dimensional, complex function. However, the Laplace transform of the 1D signal is a complex function defined over a two-dimensional complex plane, called the s-plane, spanned by two variables, one for the horizontal real axis and one for the vertical imaginary axis. If this 2D function is evaluated along the imaginary axis, the Laplace transform simply becomes the Fourier transform.


What is the use of the Laplace transform in industries?

The use of the Laplace transform in industry:The Laplace transform is one of the most important equations in digital signal processing and electronics. The other major technique used is Fourier Analysis. Further electronic designs will most likely require improved methods of these techniques.


What mathematical process can you use to transform signal waveform of frequency domain into time domain. or the other way around?

This is called the Laplace transform and inverse Laplace transform.


Application of laplace transform?

AC circuit analysis, for one.


Which type of coupling capacitor is used in RC coupling?

Capacitor coupling involves the use of coupling capacitors.Coupling capacitors are mostly ceramic capacitors.These are in the range of 0.47picofarad to 4.7 microfarad.Never use an electrolytic capacitor for coupling.It is meant for bypassing.coupling capacitors aloow AC and block DC components of a DC coupled signal.This DC component may also include noise,a grounded voltage signal or a step function.The analysis of the circuit involves determining the h-parameters of the amplifying stages,the Fourier transform of the signal applied and at various points of the circuit and the Laplace transform of the circuit sections in order to know the conditions of operations .Using complex engineering mathematics,the time varying analysis can be performed .This makes use of the Maxwell's equations to know the fields of the passive and active elements.

Related questions

What is the difference between Fourier transform and Laplace transform and z transform?

Fourier transform and Laplace transform are similar. Laplace transforms map a function to a new function on the complex plane, while Fourier maps a function to a new function on the real line. You can view Fourier as the Laplace transform on the circle, that is |z|=1. z transform is the discrete version of Laplace transform.


What is the difference between the fourier laplace transform?

They are similar. In many problems, both methods can be used. You can view Fourier transform is the Laplace transform on the circle, that is |z|=1. When you do Fourier transform, you don't need to worry about the convergence region. However, you need to find the convergence region for each Laplace transform. The discrete version of Fourier transform is discrete Fourier transform, and the discrete version of Laplace transform is Z-transform.


Why fourier transform is used in digital communication why not laplace or z transform?

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What is the difference between a Fourier transform and a Laplace transform?

Laplace = analogue signal Fourier = digital signal Notes on comparisons between Fourier and Laplace transforms: The Laplace transform of a function is just like the Fourier transform of the same function, except for two things. The term in the exponential of a Laplace transform is a complex number instead of just an imaginary number and the lower limit of integration doesn't need to start at -∞. The exponential factor has the effect of forcing the signals to converge. That is why the Laplace transform can be applied to a broader class of signals than the Fourier transform, including exponentially growing signals. In a Fourier transform, both the signal in time domain and its spectrum in frequency domain are a one-dimensional, complex function. However, the Laplace transform of the 1D signal is a complex function defined over a two-dimensional complex plane, called the s-plane, spanned by two variables, one for the horizontal real axis and one for the vertical imaginary axis. If this 2D function is evaluated along the imaginary axis, the Laplace transform simply becomes the Fourier transform.


Why Laplace transform is used in analysis of control system why not Fourier?

it is used for linear time invariant systems


What is the fourier transform of the Laplace operator of a function?

Let F(f) be the fourier transform of f and L the laplacian in IR3, then F(Lf(x))(xi) = -|xi|2F(f)(xi)


What is the use of the Laplace transform in industries?

The use of the Laplace transform in industry:The Laplace transform is one of the most important equations in digital signal processing and electronics. The other major technique used is Fourier Analysis. Further electronic designs will most likely require improved methods of these techniques.


Difference between z transform and laplace transform?

z transform is used for the digital signals and laplace is generally used of the contineous signals.


Difference between fourier transform and z-transform?

Laplace Transforms are used primarily in continuous signal studies, more so in realizing the analog circuit equivalent and is widely used in the study of transient behaviors of systems. The Z transform is the digital equivalent of a Laplace transform and is used for steady state analysis and is used to realize the digital circuits for digital systems. The Fourier transform is a particular case of z-transform, i.e z-transform evaluated on a unit circle and is also used in digital signals and is more so used to in spectrum analysis and calculating the energy density as Fourier transforms always result in even signals and are used for calculating the energy of the signal.


The Laplace transform of sin3t?

find Laplace transform? f(t)=sin3t


What are the limitations of laplace transform?

Laplace will only generate an exact answer if initial conditions are provided


What is the difference between unilateral and bilateral laplace transform?

unilateral means limit is 0 to infinite and bilateral means -infinite to +infinite in laplace transform

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