negative frequency

[charan langton]

Dear Ms.Charan Langton,

First of all , thanks for bringing up this site, its gr8.
I read about the Fourier Analysis Tutorial in which you have tried to give the picture of what it means when we speak about negative frequency and that its the second dimension ,the direction , which indicates the sign...
How do i interpret the same in time domain .
Is it that the signal which is traversing towards the right direction has +ve frequency..and vice versa...
or has it got to do with phase of a signal and in that case whats the reference with respect to which the sign of its freq is decided?

Could anyone give some more clear picture on the above.


Thanks and Regards,
Prashant

[Prashant]

I am sorry!!, the above message was posted by me

Regards,
Prashant

[sandeepmonangi]

Hai,
The negative frequencyn representation in fourier analysis is for only mathematical analysis sake .It does not interpret anything else,Ithink so.

[tadesse86]

The negative frequency has no physical meaning it is only for mathematical senses it is icluded.in communication it has no meaning.but mathematians develop the theory from double side analysis i think.

[deharphta]

Mathematics has no physical meaning, it is only for mathematical senses.
When mathematics is used to describe a physical system it takes on a physical meaning, namely the physical meaning that you give it.
But then, language has always been a bit like that.....
If you get my meaning

[yashar]

Hi
But I think negative frequency has physical meaning.
in ex. consider a rolling wheel it rotate in cw but u see it rolling ccw....why? plz think about it . ;D

[hunter006]

Negative frequency is used for mathematical processing, rather than actual useful information.

One example is that speakers aren't sold with a frequency response of negative frequencies. They're usually of the range of 20 Hz to ~22 kHz (positive domain only), representing the range of the healthy human ears at age 8-10. However, if you were to use a microphone to record any sound produced by the speakers and process it via FFT, you'd see that the frequency representation consists of both positive and negative frequencies (note this was one of the experiments I did for a DSP lab in university with CRO's that had FFT capabilities).

Simply put, negative frequencies are the consequence of the theory and mathematical processing. In terms of usefulness, the mathematics can be manipulated for information to be present under the negative frequencies (such as in the case of IEEE 802.11a).

As for the case of the rolling wheel, again that is a case of the convenience used for mathematics. Taking the base reference of CW as the positive domain, a wheel rolling in a CCW direction does indeed take on a negative frequency (radians per second). However, changing the reference point to something more suitable, say, using CCW as the baseline, with no loss of generality the math can be applied with the same result, only using positive frequency values instead of negative frequencies.

[tmcdavid]

hunter006 said:

Negative frequency is used for mathematical processing, rather than actual useful information.
quote]
On the home page of complex2real, Langton leads off with the statement "Communications is not an easy science. The math is heavy, and intuition is slow to develop. "
Several on this thread have expressed opinions similar to Hunter's to the effect that the concept of negative frequency is "only mathematical" and of little or no practical use. You all need to work on developing your intuition, as Charan Langton warns. Only Yashar showed promise of developing some intuition, though his example was not very convincing.
Radio engineers that produce single-sideband modulation and demodulation will think the notion that the negative sidebands are only mathematical is pretty silly. In seismic geophysics, the processing centers use the Hilbert transform to reproduce the analytic form of the acoustic reflections. This allows them to determine if a reflection from the interface of two rock layers was from a increased density (positive phasor rotation) or decreased (opposite phase rotation). Another acoustic example: We can take your speaker that you think only produces positive frequencies, and a pressure microphone placed between it and a solid wall, and expect to sense the speaker's sound wave and its reflection mixed. But we can add an accelerometer or a velocity mike at the same location as the pressure mike, and with a little signal processing choose to hear only the direct sound wave or the reflected one.
The reason a Fourier Transform of the wave recorded from the pressure microphone shows both positive and negative frequencies is because it it telling you the truth: that there is an ambiguity, and either could be the case. Once you obtain the quadrature component and create the analytic signal, you can combine the quadrature components to obtain the one-sided transform, as shows in the Hilbert tutorial.
A lot of people think quantum mechanics describes purely theoretical things. But in truth, reality follows the math faithfully, even though it runs counter to our native intuition.

With hopes for everyone's intuition development,
Regards,
Terry