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What is Negative Frequency!!

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Junior Member level 2
Nov 5, 2005
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negative frequency spins clockwise

here is a challenge for the gurus .i haven't been able to understand the concept of negative frequency so if anyone can elaborate it for me..

i am referring to the frequency spectrum of signals.

thanks in advance..


The negative frequency is just a mathematical method of manipulating signal, in real life, no negative frequency is available, and if analysing any signal gives you a negative frequency it''ll just be mirrored to the positive frequency domain.

Simply, negative frequency is just a method of manipulating the signals mathematically, to obtain the real results, just mirror the negative frequency to be imposed on the positive part if due to a mirror

The concept is pretty simple. Let me give you an analogy to demistify you. Consider you have have $10. Now this money can be represented as ($20)+(-$10)=$10. Now is there a -$10 currency ? Similarly a negative frequency combines with a positive frequency to give the actual frequency.

The only negative "frequency" value I can think of is a frequency OFFSET or difference.

Negative frequency is a very real thing with complex (quadrature) signals. At any instant, the signal has X and Y components (or I and Q), and that's just a vector having some magnitude and phase. A positive frequency spins the vector counter-clockwise, a negative frequency spins it clockwise. Two signals at +100Hz and -100Hz are clearly different, just as 150Hz and 350Hz are clearly different. This is highly useful in many types of communication signal processing.

Think about the wheel on your car. It's useful to know that it's spinning at 100 rpm, but it's more useful to know whether it's spinning at +100 rpm or -100 rpm. The position of the valve stem (relative to the axle) would be the X and Y components of the complex signal.

> Can anyone explain the concept of Negative frequencies clearly. Do
> they really exist?

Here's the quick answer:

If you are expressing elements in frequency space as complex exponentials
(which is the kernel of the Fourier Transform) then to have sin(kt) or
cos(kt), you have to have the sum or difference of complex exponentials at
positive and negative frequencies.

So, the time domain cosine is a real sinusoid at a positive frequency.
But, in Fourier Transform spectral space, a real cosine is made up of
complex exponentials of equal amplitude at positive and negative equal
frequencies. You can find the identity in a trigonometry book of tables.

So, do they really exist? It depends on which domain you're looking at
them. In the time domain of real signals, I'd say no. In the frequency
domain, yes because of the observation above.
The rest of the discussion on this subject can be found at:


Consider this
sin (Wo) = (exp (j*Wo) - exp (-iWo))/2
cosine (Wo) = (exp (j*Wo)+- exp (-iWo))/2

By using fourier series/transformation we know complex signals (including real signals) can be represented in terms of summation/integration of compex exponentials.

So we can see that though a negative frequency can not be defined, for fourier signal representation we need to consider negative exponentials i.e. negative frequencies.

The above explanation can be visualised using a clockwise and anticlockwise phasor used to represent a sine wave.It is similar to e.g. of negative rpm mentioned somewhere above.

When you determine transfer characteristics your poles and zeroes can be negative or positive, which have a great inmpact on circuit stability and other characteristics...

You can read "Signals and Systems" by Oppenheim.

in some communication processes -ve frequencies of real +ve frequencies -ve frequencies exists..
in frequency domain it apear with same amplitude but opposite to the original signal.
conjugate of your signal is also -ve frequency of the original signal...

ranjeeth said:
sin (Wo) = (exp (j*Wo) - exp (-iWo))/2
cosine (Wo) = (exp (j*Wo)+- exp (-iWo))/2

To be more precise ;-) :

either "i" or "j" should be used for the imaginary unit, not both in one expression

sin(ωo) = [exp(jωo) - exp(-jωo)]/2j
cos(ωo) = [exp(jωo) + exp(-jωo)]/2
(not +-)

3) although physical signals can be represented by complex exponentials, the signals themselves are always real, i.e. the resulting expression (compound of complex components) has a pure real value.


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