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do frequencies have negative values

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

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  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. DBLEXPOSURE

    DBLEXPOSURE Guest


    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?
     
  3. 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 Masta

    Bob Masta Guest

    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
    www.daqarta.com
    Home of DaqGen, the FREEWARE signal generator
     
  5. Jasen Betts

    Jasen Betts Guest

    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
     
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