do frequencies have negative values

Well, common scene is telling me that there is no such thing as "negative frequency". That would be saying that a wave is not doing anything at a particular rate. Could your negative numbers be telling you the your answer is "less than" some other referenced frequency?

The transform is done by multiplying the incoming waveform by sine and cosine waves at each spectral line frequency, and averaging the results for each line. There is typically nothing to synchronize your incoming wave to the phases of the transorm waves, so the results are unpredictable as far as how much of each sine or cosine component you see, (That's why we usually look at magnitudes of real inputs.)

But yes, you can have a negative frequency and it does (sort of) make sense physically. The case where you are most likely to run into this is with frequency modulation where the modulator's negative swing is larger than the carrier center frequency. The modulated output wave goes to DC and then appears to "reverse direction" as the frequency goes negatrive.

You can see all this for yourself with my freeware DaqGen signal generator, using the FM modulation option. Let me know if you have any questions about this.

Best regards,

Bob Masta dqatechATdaqartaDOTcom D A Q A R T A Data AcQuisition And Real-Time Analysis

Hi,

Negative frequencies are simply a mathematical slight of hand in the same way that +6 may be represented by the sum of +11 and

-5. In the usual Fourier transform of a periodic waveform, cosine and sine terms are generated along with their coefficients. If we use the standard exponential identities...

Cos(x) = 1/2(exp[jwt] + exp[-jwt])

Sin(x) = -j/2(exp[jwt] - exp[-jwt])

...in place of these, a series emerges with complex coefficients and terms including both w and -w (with the real and imaginary components being normally drawn on separate diagrams). The negative ones however, have the same physical presence as minus five apples has in a school arithmetic lesson. It is just that in combination with the other terms a tangible waveform emerges.

Having said all of that, if you regard a phasor as a counter-clockwise rotating line at a particular frequency then a negative one of the same frequency would be a line revolving clockwise at the same rate. It is easy enough to think up physical models (e.g. motor shafts) where this could be a useful insight. The problem is that we usually think in terms of time which, as far as we know, goes only one way. How about then substituting some other variable that doesn't have this limitation? The maths would be just as valid.

I would have gone on a little longer but it is Friday and I must make the local fish 'n chip shop before they close or I'll starve.

Cheers - Joe

could it be out of phase?

Hi, i thank u from the bottom of my heart for your explaination. this question was haunting me for a looooooong time.

-BZ