negative frequencies

[fisico]

can someone give me a convincing argument of why negative frequencies are useful?

thanks!

[johnpool]

This is pretty much like asking: "why are negative numbers useful?".
I think the answer is simple: they just make your life a little easier.

[aya2002]

as i understand it is the image of the positive frequency

[lutzvw]

The question was posted here in the forum about two years ago, however, I feel that it is still not answered.
Let me try:
1.) There are no negative frequencies in reality! They are only a fiction (which makes - as stated above- life a bit more easy).
2.) What does this mean: More easy?
The most important example is the FOURIER expansion of periodic signals. Using the EULER expressions for all (co-)sinusoidal parts of the spectrum (complex FOURIER seris) it is very easy to formulate and calculate the spectral distribution if compared with real FOURIER series.
However, in this case it is necessary to invent some negative parts in the spectral distribution, which are called "negative frequencies".
Thus, the formal invention of negative frequencies makes life (calculation of the spectrum) more easy.

Addendum: Just now I have discovered that this subject is extensively discussed in TUTORIAL 5. Sorry - it was long time ago that I have visited this forum. I will correct this in the future.

[sharabasi]

Can someone help me with that question,

are signals in in base band always symmetric, Or is it only in the +ve frequency axis and we mirror it in the negative side ??

Thanks

[RickLyons]

Hello,
to see how the notion of negative frequencies can be useful to us, you might take at

www.dspguru.com/sites/dspguru/files/QuadSignals.pdf

[-Rick Lyons-]