Negative Frequency - What is it?

[lmtalsoul]

I've been thinking a lot but in vain.

1. Can someone explain me clearly what exactly does the term Negative Frequency mean?

2. Does it really exist? What is its significance?

3. What could have been the scenario if there wasn't negative frequency concept?

Please Help.

 

[IanP]

Whatever you call "negative" has been developed to support certain theory ..
Say, you have 2 apples - can you imagine (-2) apples --> I can't ..
However, negative numbers are commonly in use - not because they "physically" exist, but because it is very "convenient" to have for "manipulations" ..

The same story is with the negative" frequency concept ..
Can you imagine something rotating (-1)Hz --> again, I can't, this object will be rotating at 1/s angular speed, but to mark the direction of rotation one will use the (-) sign ..
Here you can find explenations on what is called "negative" frequency:
https://en.wikipedia.org/wiki/Negative_frequency

Regards,
IanP

 

[lmtalsoul]

Thank you so much Sir. I've read that Wikipedia Article. But I don't seem to have understood something. I mean, I missed out something.

Even if it was meant to "simplify" calculations, does it mean that it doesn't have any significance and that besides being used to simplify equations, it is a useless concept?

And one thing, if there is a negative frequency spectrum in fequency domain, what does it really mean in time domain? After all, time domain and frequency domain are just the same terms, same things being represented in two different ways.

I'd be really grateful if you can help me out in this regard.

 

[neils_arm_strong]

It is just for convineince.If there is a low pass signal and it is multiplied by some high fregency signal,then its spectrum shifts to the right.If you consider the shape of the spectrun of that signal then it is symmetric about the high frequency that was multiplied.Then if it was low pass signal ,then also it should have been symmetric.Isn't it?.So to explain such observations negative frequencies are used.

 

[riku]

hi...........
the -ve frequency just show symmetry ............ and the easyness of the problem.........it has no physical significanse............ u can start it zero.........but at that time ur calculation is complex but u will get the same result......... that's why we go for -ve frequency in any problem especially in graph work:|

 

[electron_boy]

hi
the negative frequency is 180 out of phase. it is like having two wheels rotating in either direction as said in wikipedia

 

[electronics_kumar]

negative is not existing..it is menat for easy understanding and manipulations

 

[JoseLeonardo]

There arent negative frecuency, is only math theory, but if you want leanr more, read Signal and Systems by Oppenhiem

 

[saberbf]

the frequency domain is defiened on the base of sinusoidal waves (Fourier transform), since in a sine wave there is exp(jw) and exp(-jw) components, to ease implementation this exp functions in freq. domain, the Negative freq. is defiened. that is, there is no Negative Freq.

 

[ashischatterjee]

Negetive frequency is nothing but a mathametical fallasy.

If ,exp(jω)= exp (-j5) then we can conclude w=-5
exp(-j5)=cos5-jsin 5
A signal is being represented by two orthogonal components.
Nothing more than that.

 

[hans_mauritz]

Negative Frequency...????
There isn't a negative frequency, because frequency isn't a vektor and the negative here means direction.

 

[louisnells]

Think of a vector rotating in clockwise direction. It has a period of rotation and hence frequency. Now think of the case with the same vector rotating in anti-clockwise direction with same speed. In this case too there is both the same period and frequency.

The only difference is their direction. In reference one of the vector rotation the other one is rotating in the -ve direction. Its actually upto your direction, you can choose one as the +ve direction.

 

[starfish]

Negative frequency is a very real thing in Digital Signal Processing / Communications applications. Think of two complex exponentials

x1 = exp( + j wo n )

x2 = exp( - j wo n )

During modulation a lower frequency signal is multiplied by a higher frequency signal. So when u multiply ur signal of interest with x1 then the spectrum shifts in one direction. If u multiply ur same signal with x2 then the spectrum shifts in the other direction. Both x1 and x2 have the same frequency ' wo ' but one is positive and one is negative and its effect is very evident from the above modulation example.

A physical example could be of a Fan which is rotating Clockwise with 25 rev / sec and another Fan rotating Anticlockwise with 25 rev / sec . So frequency of rotation of the fan is the same in both cases but the direction is exactly opposite.

 

[mzzzzb]

from my point of view negative frequency is a concept associated with exponential fourier transform/series

to begin with lets talk about the trignometric fourier transform, it says that almost every finite signal can be expressed as a sum of sinusoids with varying frequency from 0 to +∞, no negative frequency here. whats good about working in frequency domain is that it is easier to understand and define characteristics of filters and like. whats bad about trignometric series is that it is hard to manupulate them, take multiplication of two sinusoids, it is not straight forward, take complex exponentials, they are easier to manupulate, easier to multiply, divide, differentiate and integrate and like sinusoids they are eigen functions of linear time invariant systems ie if you send a c. exponential down a LTI you will get a c. exponential with same frequency possibly with different amplitude and/or phase.

now to return to the point, exponential fourier transform lets us express any signal (real or complex) as a sum of complex exponentials A.e(jwt+Φ) with varying frequencies ranging from -∞ to +∞. why negative? because e(jwt) is essentially complex in nature, it has both real and imaginary parts and we need to construct purely real signal just by summing them, this is only possible when imaginary components cancel themselves out. now you must remember one property of fourier transform that for real signals X(jw)=X*(-jw) ie for every positive frequency component A.e(jwt) there is a negative frequency component A*.e(-jwt) where A is in general complex(gives both magnitude and phase). you can work out the details but the result tells us that every time the imaginary component gets cancelled away and we are left with the real terms only. so use of negative frequency allows us to use complex exps. to represent perfectly real signals. here negative frequency is strictly related to complex exps. only, there is no sines and cosines with negative frequency. and i am talking signals/communications point of view. in my opinion the frequency used in mechanics: circular motion, shm is different from this.

i would like to comment on the symmetry of sprectrums of real signals. you can see the magnitude spectrum is perfectly symmtric and the phase shows odd symmetry about the zero frequency axis. this is exactly the case with transfer functions of real systems. if the signals were complex this symmetry won't be there. what i mean to say is that you don't have independent control over negative frequency components, for real signals their shape is already determined when you define the positive counterpart. this is why when we talk about bandwidth of a signal or system we talk only about the positive frequency components.

now to the existence of negative frequencies, yes you cannot generate signals that have only negative frequency components(neither can you generate signals with strictly positive frequecies) from any worldly signal generator but observe in AM (double sided ones) you can see two side bands symmetrically sitting about the carrier freq., the lower sideband is the manifestation of the negative frequency component. nature loves symmetry and negative frequecies gives us the symmetry in this case. to really appreciate the elegence of this please look for use of complex envelop for low pass analysis of band pass signals and systems.

this is my opinion, hope this answers your questions!

 

[shriramdevi]

as told previously fpr mathematical convinence we use exponents n in order to "remove" imaginary part of it we use sum of two exponents ( lik we use cosφ = .5*(exp(φ)+exp(-φ)) ...
this also tells why amp. of all freq. is halved when we plot complex freq. spectrum while its original mag. is shown on when we plot mag plot for freq. > 0

 

[itzikhaim]

Hello there !

Please see the already discussed topic, here at EDA:

 

[shbakram]

good discussion