frequency modulation

[sanctus]

I'm more on the theoretical side (even if that might be not a good excuse for the following question) and was wondering why usually a frequency modulated source has the oscillating term of the form
1)?

And not of the form
2)?


Is it just because if one measure a phase difference through an absorbing material for example (and uses a signal of the form 1) as reference as well), in case 1) the phase difference will be in the positive direction (as long as the phase difference is small enough) and in cas 2) in the negative direction? With positive (negative) direction I mean, for a small enough phase difference, the peak shifted in the positive(negative) direction with respect to the reference signal.

If all above is right, is there actually any measurable/detectable/physical difference between case 1) and case 2) ?

[snoopy]

Originally Posted by sanctus

I'm more on the theoretical side (even if that might be not a good excuse for the following question) and was wondering why usually a frequency modulated source has the oscillating term of the form
1)?

And not of the form
2)?


Is it just because if one measure a phase difference through an absorbing material for example (and uses a signal of the form 1) as reference as well), in case 1) the phase difference will be in the positive direction (as long as the phase difference is small enough) and in cas 2) in the negative direction? With positive (negative) direction I mean, for a small enough phase difference, the peak shifted in the positive(negative) direction with respect to the reference signal.

usually the fm signal is given by


I have never seen it expressed in imaginary numbers before but
I am guessing its always -i because otherwise you wouldnt get a positive result otherwise.

Sorry I couldnt be more help but its been way back to college for this one as I dont deal with transmission problems.
maybe if you gave the full set of equations we could figure it out between us.

Peace

[sanctus]

To me it seems the most intuitive way to describe a modulation: the exponential shows the phase turning...but I can't see this intuitively in the way you say a fm is described (I do not say you are wrong, just that I find it less intuitive).

Did I get you right you say that the only reason to have "-i" and not "+i" is to have a positive phase shift?