transform

[ajaydhingra]

what is the difference between fourier transform and laplace transform
kindly mention the physical significance

[Ankit Modi]

Laplace transform converts a signal from "Time Domain" to "s-domain", whereas Fourier Transform converts it to "Frequency domain". Basically all these transforms were defined to "ease" the analysis of a signal. like u see if u have to perform convolution in time domain then its tedious. Multiplying the time domain signal with exp(-s*t)- as in Laplace transform or with exp(-2*pi*f*t) as in Fourier transform, converts multiplications to additions.
You can just think of it as different domains depending of the variables you use in your exponetial. same for Z-transform, which will convert the signal to z-domain.
As said by some, these transforms are different "bridges" over which you can easily cross the river of "time domain"-wthiout getting drowned.
I hope this helps. I know this is bit confusing, actually people have made so many different bridges(transforms) that now instead of getting drowned in the river, one gets lost in the maze of these bridges!! ;D

[Charan Langton]

In mathematical terms, the Fourier transform is a superposition of exponentials of the type ejwt (which are sinusoids) and the LaPlace is a superposition of the exponentials of the type est which are not necessarily sinusoids.

The Fourier transform is generally used in situations where the signal is periodic. The continous version of Fourier transform is the Fourier series and the DFT is its discrete version. The discrete version of LaPlace transform is the Z transform.

We use Fourier tranform in cases where there is a significant periodic content such as a carrier. LaPlace transform is used where most of the signal is aperiodic, such that the signal does not decay with time, i.e it does not go to zero, e.g. x2 or the unit ramp function. LaPlace also has the ability to bring out poles and zeros of a function, hence it has better resolution than the Fourier transform. And most importantly, LaPlace uses a much simpler notation, a continous variable s which makes the math easier.

But I guess you could say that the main difference is that LaPlace tansform would be used where we may see unstable behavior. An example is the use of LaPlace transform in the study of Phase Lock Loops, where we have both steady-state and unstable conditions.


Charan Langton
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