Re: fourier transform
Let me explain the thing in a different way!!!
The FT of a signal \[x(t)\] is given by the formula
\[X(j\omega)=\int\limits_{-\infty}^{\infty}x(t)e^{-j\omega t}dt\]
By closely looking at the equation we can see that we are actually finding the cross-correlation,, at origin, between the signal \[x(t)\], which may consist of infinitely many frequencies, and the signal \[e^{-j\omega t}\] which has only one frequency \[\omega\] of course for a given \[\omega\]. Now let us see quantitatively for various values of \[\omega\] on \[x(t)\].
If \[\omega \] is small and the signal \[x(t)\] varies slowly then we can intuitively see that the integral value is large which says that there is high correlation between \[x(t)\] and \[e^{-j\omega t} \] at \[\omega \]. How much correlation i.e., the measure of the correlation is given by the number \[X(j\omega)\]. So for slowly varying signals this value will be large for low values of \[\omega \] and small for large values \[\omega \]. Or in other words we can say that \[X(j\omega)\] gives the measure of frequency content in the given signal \[x(t)\].
Hope I think I have tried to explain the FT relation in an intutive way.