Question

what is the difference between fourier transform & laplace transform

Answer 1

(1) laplace transform is used to shift the system transfer function from time domain to the frequecy domain. in fourier transform we get the frequency spectrum of the signal (i.e) the variuos frequencies in the given composite signal and their relative amplitude or gain. in laplace the 't' is replaced by (sigma+j*w) The real part help us to plot the poles and zeros of a given system. In fourier we are mostly interested with the variations of the gain of variuos frequency components in signal and fourier transform is used to break up signal into the corresponding harmonics of the fundemental frequencies.

another one is
(2) IN LAPLACE TRANSFORM THERE IS CONCEPT OF REGION OF CONVERGENCE BUT IN FOURIER TRANSFORM THERE IS NO CONCEPT OF REGION OF CONVERGENCE AS S=SIGMA +JW IN LAPLACE TRANSFORM BUT IN FOURIER TRANSFORM WE PUT SIGMA=0(THIS IS THE MOST IMPORTANT DIFFERENCE) .REGION OF CONVERGENCE IS VALUE OF SIGMA FOR WHICH LAPLACE INTEGRAL CONVERGES (THIS PART NEED MORE CLARIFICATION IT IS QUITE DIFFICULT TO MAKE YOU UNDERSTAND THIS PART WITH OUT A PEN AND COPY)
and the final one is ----------
(3) LAPLACE TRANSFORM IS A MATHEMATICAL TOOL USE TO MAKE OUR CALCULATION EASY. IN TIME DOMAIN THERE ARE CERTAIN EQUATION WHICH ARE TOO BIG TO SOLVE IN TIME DOMAIN SO WE CONVERT IT INTO S DOMAIN FOR EASE OF CALCULATION AFTER THAT WE TAKE INVERSE LAPLACE TO CONVERT IT INTO TIME DOMAIN AGAIN..................BUT FOURIER TRANSFORM IS A SIGNAL ANALYSIS TECHNIQUE IT HELPS US TO ANALYSIS THE SIGNAL IN FREQUENCY DOMAIN WE CHECK THE VARIOUS CHARACTERISTICS OF SIGNAL FROM ITS FREQUENCY SPECTRUM.....