Frequency domain --------amplitude and frequencies.

I have studied time domain where you specify different amplitudes of the signal at different times.
I know the meaning of amplitude.

But when it comes to frequency spectrum what are you doing?

You have amplitude here also. What is this amplitude?
I don't think this amplitude is same as that of that amplitude.

For example: if time domain has a sine wave it has only one frequency. So I believe that we have only one frequency in the frequency domain. But the amplitude is an impulse. It is infinite but at the same time I am writing the coefficient of direct as its amplitude. Besides I can't understand the impulse function clearly. I mean what happens to impulse function s(t) when t=0. Does that become infinity or one?

In addition we also have a frequency in the negative side. I mean we have two frequencies instead of one frequency. What does that mean? I mean what do you mean by negative frequency?

If you can't understand the question you can tell me.

Thanks in advance.
:-D:-D:-D:-D:-D

the negative frequencies come from the following:
e^jwt = cos(wt) +j sin(wt)
Re(e^jwt) = cos(wt)
cos(wt) = 0.5(cos(wt) + j sin(wt)) + 0.5(cos(-wt) + j sin(-wt)) = 0.5*e^jwt + 0.5*e^-jwt
sin(wt) = 0.5(cos(wt) + j sin(wt)) - 0.5(cos(-wt) + j sin(-wt)) = 0.5*e^jwt - 0.5*e^-jwt

the FT assigns coefficients to a set of terms in the form a_n * e^j*w_n*t.
the idea is that a function can be expressed in terms of an infinite series of complex exponentials. If the input is a real-valued function, then it will be a sum of sines and cosines. In this case, the coefficients will follow a_{+n} = a_{-n}*. where a_n is a complex scalar value, and a* is the complex conjugate. in this case |a_n| is the amplitude. for real signals, sometimes |a_{+n}| + |a_{-n}| is listed as the amplitude. It is common to see only positive frequencies listed for some applications. In such cases it is also common to see the plot scaled so that integration can be done by only using the positive frequencies. (eg, for integrating |X|^2 to determine signal power). In these cases, it is assumed that the reader will convert the transform into a valid representation if needed.

the impulses are actually "distributions", as they don't meet the strict definition of a function. It is a way to represent a finite amount of area in an infinitely narrow rectangle. In this manner integrating to find "the area under the curve" will works even with the impulse, and there is no need to claim any more than exactly one frequency is in the input (eg, due to some minimum rectangle width). For this reason, they are listed as "infinity" with a weight equal to the area inside the infinitely long, infintesimile wide rectangle.