The physical significance of negative frequencies

[Old Nick]

jsin wt signal

What does "ve" mean?

-ve is a common abbreviation of negative,
+ve is positive.

 

[echo47]

negative frequencies

Ok thanks, a new term for me.

My scope is probably similar to yours. It doesn't have any built-in vector or quadrature measurements. I have to interpret the waveforms visually. Or I could download the waveforms into my computer and analyze them there.

My approach to negative frequency resembles this article in RF Design. Look for the sentence, "negative frequency can be given a solid physical meaning by defining it properly in the context of complex, or quadrature, signals."
**broken link removed**

I may be demented, but I'm not alone!

 

[Old Nick]

Re: negative frequencies

Ok thanks, a new term for me.

My scope is probably similar to yours. It doesn't have any built-in vector or quadrature measurements. I have to interpret the waveforms visually. Or I could download the waveforms into my computer and analyze them there.

My approach to negative frequency resembles this article in RF Design. Look for the sentence, "negative frequency can be given a solid physical meaning by defining it properly in the context of complex, or quadrature, signals."
**broken link removed**

I may be demented, but I'm not alone!

It's a shame the figures etc. that are referenced in that article are not present. But apart from the sentence you've highlighted (and even in that too), it's all talk of abstract concepts. Describing and abstract concept using other abstract concepts doesn't make it real.

I've always had my suspicions about RF engineers.

 

[echo47]

negative frequencies

Near the top of that web page, "click here for article" gives a PDF. Unfortunately some parts are fuzzy/unreadable.

 

[LvW]

Re: negative frequencies

It sounds like you are unfamiliar with complex (quadrature) signals. The signal has two orthogonal components, I=cos(2*pi*f*t) and Q=sin(2*pi*f*t).

Perhaps I misunderstood something - and I am happy to learn something new,
but for me it sounds that perhaps you simply have mixed a phase shifted signal with a "neg. frequency". Or what else is the difference between sin and cos ?

 

[echo47]

negative frequencies

It's not just a phase shift. The two components are orthogonal. The RF Design article gives a brief introduction to the concept. Applying that concept in various useful ways is a full field of study in college.

 

[LvW]

Re: negative frequencies

OK, thanks to pointing my attention to your contribution in “rfdesign”. In this excellent article you have defined a negative frequency as a sinusoidal wave shifted by 180 deg with respect to the original signal.
(Quote: For now, the definition of the -600 Hz sinewave is one whose phase is shifted by 180° relative to a +600 Hz sinewave).

And this is the answer to my question posted above (June 29th, 10:57).

And, at the same time, this clarifies our different positions – as your argumentation is based on the following simple rule: sin(-wt)=-sin(wt).

Now coming back to the question from rebelstar who has started this topic - I´ll try again an answer:
Of course, the inverted sinewave –sin(wt) has a physical meaning – and therefore also the identical expression sin(-wt). But, I think the original questions remains still unanswered, namely if the expression within the brackets alone (-w) has a physical meaning by itself.

Final note: I am sure, this discussion can be of great value for some visitors of this forum because they can learn about the importantance of a common understanding when discussing technical parameters and definitions.

 

[echo47]

negative frequencies

The 180-degree shift explanation is useful at that point in the article, but I don't think it has reached a complete, practical conclusion. You can't examine an isolated sinewave and determine its phase unless you also have some sort of reference signal. I think that's why the article's paragraph added the words "for now".

A quadrature signal provides its own reference, so to speak. The signal's two components are I=cos(2*pi*f*t) and Q=sin(2*pi*f*t). It's easy to examine those waveforms, observe the inverted sine component, and determine if f was positive or negative. (see my scope snapshots)


Complex signals, quadrature, and negative frequency are powerful engineering techniques, used throughout modern communications and signal processing systems. As for whether or not such concepts have "physical significance", well I'm not going to discuss that anymore, each person can decide that for himself!

It's unfortunate that those wonderful techniques use terms such as "imaginary", "complex", "j", and "e^jωt". Those terms have scared away a lot of students simply because they sound abstract and difficult.

 

[LvW]

Re: negative frequencies

It's easy to examine those waveforms, observe the inverted sine component, and determine if f was positive or negative. (see my scope snapshots)

It´s a pity, I was of the opinion we would be on “one line” now. You may argue that I´m fighting with abstract words, but – as I have mentioned – I like exact and clear definitions.
And, therefore, let me say that I cannot see “frequencies” in your snapshots. What I can see are time functions, i.e. voltages with changing values according to a sine function having a certain period from which I can calculate a corresponding frequency. More than that, I realize that perhaps one function is the inverse of another function and, therefore, you can allocate a “minus” sign to it. Thus, we have a negative function.
But, the period resp.the corresponding value of the frequency itself is not a function but a property of this (possibly negative) function. And counting the periods gives a positive number.
Is there anything wrong in my argumentation ?

 

[echo47]

negative frequencies

My oscilloscope snapshots are measurements of actual quadrature signals of +500 Hz and -500 Hz.

We seem to be communicating on different wavelengths. I'm not sure how to continue. Sorry, I give up!

 

[LvW]

Re: negative frequencies

We seem to be communicating on different wavelengths. I'm not sure how to continue. Sorry, I give up!

Communication should be not a problem if anybody tries to answer questions from the other side. My last question was simply if something in my argumentation was wrong or not.
It´s really a pity, for my opinion two engineers should find a common base to communicate. And more than that, it´s not a good example for newcomers.

 

[echo47]

Re: negative frequencies

Hi LvM, I tried again to follow your train of thought in your previous message, but you really lost me!

Here's how I read the frequency of a quadrature signal such as my two oscilloscope snapshots. For simplicity I'm pretending the amplitude is 1.

1. A simple quadrature signal has two components: I=cos(2*pi*f*t) and Q=sin(2*pi*f*t). I connect the scope probes so I is the yellow trace, and Q is the cyan trace.

2. I examine the two component waveforms, and determine the value of f that satisfies the two quadrature component equations. To do that, I first measure the frequency of either component by using conventional oscilloscope techniques, and then I determine the sign (positive or negative) of the quadrature signal's frequency by observing the relative phase between the two components. If I leads Q, frequency is positive. If I lags Q, frequency is negative. That's ordinary behavior of cosine and sine.

Examples:

First snapshot: The component period is two divisions at 1ms/div, or 500 Hz. I leads Q, so the quadrature signal's frequency is positive, +500 Hz. The equations are I=cos(2*pi*500*t) and Q=sin(2*pi*500*t).

Second snapshot: The component period is two divisions at 1ms/div, or 500 Hz. I lags Q, so the quadrature signal's frequency is negative, -500 Hz. The equations are I=cos(2*pi*-500*t) and Q=sin(2*pi*-500*t).

 

[LvW]

Re: negative frequencies

Thank you for the message. I propose to continue on a "personal message" base.
LvW

 

[rebelstar]

Re: negative frequencies

HEllo all,
thank you all so much for your replies.the discussion has been useful.

In the mean time , i came across this very useful article which has cleared some doubts in me (or rathet made me even more inquisitive)

**broken link removed**

Right now,based on the discussion and the article,i think that,
negative frequency might be a 180 deg phase shifted signal.



If we consider the frequency vectors e^jwt and e^-jwt rotating in the complex plane,we see that they are moving in opposite directions.

I get one more doubt..
Can Cos(wt) itself be expressed as a Cosine and a Sine wave.( ampitude of .5)
because

Cos(wt) = .5( e^jwt +e^-jwt)

This is nothing but cos(wt)+jsin(wt) and cos(wt) -jsin(wt).

Each one is a complex signal which can be represented in complex plain.

But i need to think more before it becomes clear!!.
Thank you all..

 

[khubaibahmed]

Re: negative frequencies

First of all you must know what the Fourier transform and Fourier series do with the signals.

In mathematics we have a gr8 art of splitting something (signal, systems, etc.) into "linear combination of orthonormal basis". this representation allow us to have a good insight of that.
We use same concept in almost all transforms including Fourier series.
SIN(nwt) and COS(mwt) are orthogonal for integral multiples of "w" we use them as orthonormal basis in Fourier series. We

compute an inner product (see details in linear Algebra) of signal (of which we want to compute Fourier Series) and COS(nwt).

This inner product provides us projection of available harmonic(integral multiples of "w") in signal as coefficient of

Fourier series. Thats y we get "DISCRETE SPECTRA" (not continuous) and no negative frequency.

Solution for having continuous spectra we use Fourier tarns form.

Theoretically we need two basis function to represent a unique frequency in real world. i.e

cos(?t)=\[\frac{1}{2}e^{j\omega t}\]+\[\frac{1}{2}e^{-j\omega t}\]

similarly we perform an inner product of the signal with orthonormal basis.
\[X(e^{j\omega})=\int_{-\infty}^{\infty} x(t)e^{-j\omega t}dt\]

a unique frequency returns two projections (a positive and a negative) thats y we get negative frequencies.

Why we get a shifted spectra [negative+positive] portion of transform in modulation I'll answer later

 

[FvM]

Re: negative frequencies

I doubt, if the popular oscilloscope examples and similar are really connected to the mathematical concept of negative frequencies. To my opinion, they rather confuse it.

 

[Communications_Engineer]

Re: negative frequencies

OK, thanks to pointing my attention to your contribution in “rfdesign”. In this excellent article you have defined a negative frequency as a sinusoidal wave shifted by 180 deg with respect to the original signal.
(Quote: For now, the definition of the -600 Hz sinewave is one whose phase is shifted by 180° relative to a +600 Hz sinewave).

And this is the answer to my question posted above (June 29th, 10:57).

And, at the same time, this clarifies our different positions – as your argumentation is based on the following simple rule: sin(-wt)=-sin(wt).

okay even if I try to believe you than what about

cos(-wt) = cos(wt)

So are there negative frequencies for Sine only?

I also think some people here are confusing negative frequency with complex frequencies