significance of negative frequencies in fourier transform.

[girish kakalwar]

what is the meaning of 'negative' frequency. Is there any practical meaning or its a mathematical explanation??
what is its importance?? i m very confused with this concept.
If there is no practical meaning then why do we include these frequencies in energy/power calculation of the signal.

 

[LvW]

Some time ago this subject has been already extensively discussed in this forum. Try the search function.

 

[girish kakalwar]

thanks bro... but why do we use these frequencies for energy or power calculation when there no practical meaning.??

 

[permute]

any real-valued function will have conjugate symmetry -- the real portion of the transform will have even symmetry, and the imaginary portion will have odd symmetry.

Many signals in undergraduate studies are real-valued, so this isn't an issue. Indeed, in many fields only real-valued signals are considered. This leads to a common practice of representing the transform only with the positive frequencies (scaled appropriately).

However, the negative frequencies do have a meaning. The most obvious case is for amplitude modulation. In this case, the carrier and message both have positive and negative frequencies. This leads to an upper and a lower sideband -- the message is shifted up by +fc and down by -fc because +fc and -fc are the positive and negative content of the real-valued carrier. Many other aspects of signal processing for communications will involve complex valued signals (see coherent demodulation for an example of a system that takes a real input and produces a complex output).