May i know when to use eqn like X(W)= integ from oo to -oo x(t)e^(-jwt) dt and x(t) = 1/2pi integ from oo to -oo X(W) e^(-jwt) dt?

note: oo (infinity) -oo(- infinity)

Please advise. Thanks.

 

You use Fourier Transform (FT) to convert from the time-domain to the frequency-domain. This is helpful in breaking up a time-signal into it's frequency components, since all signals can be broken down into various sinusoids of different frequencies.

For your second formula (Inverse FT), it should be dw not dt since X(W) is a function of w.

 

There are lots of reasons to use the Fourier transform. If for instance you have a need to perform a convolution in the spatial or time domain, then it is easier to convert to the frequency domain, do a multiplication, then convert back. Basically a convolution in the time domain equals a multiply in the frequency domain. There are many of these type equivalencies. This is very common, because filtering in the time domain is often performed by convolution.