# do frequencies have negative values

Discussion in 'Electronic Basics' started by [email protected], Sep 1, 2005.

1. ### Guest

hi,
why do i get a negative frequency in fourier transform of sinusoidal
wave ? arent frequencies supposed to be +ve ? i have read a few books
and they suggest that -ve frequencies are present for complex
sinusoids. so is it possible to physically generate complex sinusoids ?
-bz

2. ### DBLEXPOSUREGuest

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
is "less than" some other referenced frequency?

3. ### Joe McElvenneyGuest

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

4. ### Bob MastaGuest

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

Best regards,

Bob Masta

D A Q A R T A
Data AcQuisition And Real-Time Analysis
www.daqarta.com
Home of DaqGen, the FREEWARE signal generator

5. ### Jasen BettsGuest

could it be out of phase?

6. ### Guest

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