Negative frequencies in spectrum analysis

[sukh_ece]

Negative frequencies in spectrum analysis...

Hello everyone...
When we do the frequency analysis of a signal using Fourier transform, we get spectrum at negative frequencies also. What are they and what is the physical significance of such frequencies? Its hard for me to imagine a negative frequency. Plz share ur knowldge on this...

 

[mfb]

If your signal is real, you can ignore them - they are the same as the positive frequencies.
If you have a complex signal, they are similar to the positive frequencies, but correspond to a different "rotation" of the signal in the complex plane.

 

[the_emi_guy]

Negative frequency, like negative distance, seems non-physical. However, we can locate physical points by position relative to some arbitrary zero reference, like on the X-axis. Negative simply means "to the left of the zero reference".

It is the same with frequency. When we discuss modulation of an RF carrier, is it very convenient to consider frequencies relative to the carrier. Negative frequencies are simply to the left of the carrier on the spectral plot.

Consider measuring the angular frequency of a clockwise rotating wheel that is illuminated by a strobe light that flashes at 1Hz. My observed (measured) frequency will be relative to 1Hz. If the wheel's angular frequency is 1Hz, I will observe 0Hz, i.e. it will appear stationary. If it is rotating 1.5Hz I will measure +0.5Hz. If it is rotating at 0.5Hz I will observe -0.5Hz, negative because it appears to be rotating counterclockwise.

The strobelight here is analogous to the 2.45GHz carrier on a WiFi signal. We observe the modulation behavior relative to this carrier.

 

[sukh_ece]

Thanks @mfb and @the_emi_guy...

If we can ignore the negative frequencies for a signal...then there is one doubt...
The bandwidth of a signal ranging from -fm to fm is 2fm...then why we consider negative frequencies in finding the bandwidth...

 

[mfb]

That is just a definition of "bandwidth" - you could use half the bandwidth as "bandwidth" as well, if you add this factor of 2 everywhere else.

 

[sukh_ece]

@mfb...thanks...
I don't understand ur answer...where we can add the factor 2?...different frequencies contribute to the signal formation...a signals energy is equal to integration of the square of spectrum over entire frequency range (Parsevaals theorem)...that means negative frequencies exist and contribute in the energy of the signal ...then how can we ignore their contribution in the bandwidth...

 

[mfb]

where we can add the factor 2?

In the definition of "bandwidth". Don't do that, but it would be possible.

then how can we ignore their contribution in the bandwidth...

Maybe "ignore" is not the best word. If they are exactly the same as the positive frequencies, they don't add new information about the wave. You can just take the positive part, and multiply it by 2, as the negative part and positive part are the same.

 

[sukh_ece]

Thanks...