hello ,

i have a doubt in time frequency conversion ... why a rapidly changing signal require a large bandwidth..

why a very high frequency sine wave it self appears as a impulse at that particular frequency in frequency domain ,since it is rapidly changing with respect to time it should occupy a high band width but instead its representation is only a impulse in frequency domain.

and the other doubt is , consider a sine wave of fixed frequency but varying amplitude as a function of t. for this how the spectrum in frequency domain look like

i consider tha answer to be for the last question as a impulse at that particular frequency whose amplitude varies

You may want to look into text books and lecture talking about fourier transform and FFTs as well a modulation schemes

Here is a start

http://www.youtube.com/watch?v=ObklYbQaX24

Here is another resouce

http://en.wikipedia.org/wiki/Amplitude_modulation