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Is there any method(circuit) to retain only the positive frequency components of a signal?

thanks in advance.

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Is there any method(circuit) to retain only the positive frequency components of a signal?

thanks in advance.

- #2

Averagesupernova

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What is a positive frequency component?

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I am looking to eliminate the component at -f.

(d(t)=delta function)

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I understand what you are trying to say. But, what i was looking for is a means of eliminating the original negative frequency component in the modulating signal without having to shift it by the frequency of the carrier. In other words, i don't want any frequency components towards the left half of the y axis in the frequency spectrum.

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Why the need to eliminate the negative part of a signal?

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On a related note, do the negative frequencies constitute half of the total signal power?

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Averagesupernova

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- #9

chroot

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You can move to a one-sided spectrum if you wish, with no loss of generality, but that's just a mathematical trick. You don't need to design any real, physical device to discard the negative frequencies; they're all in your head from the beginning!

- Warren

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Warren, Are you saying there is no physical significance attached to negative frequencies?

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Which energy is defined as negative frequency and which is defined as positive depends on the timing (phase) of the FFT function itself, and is not some independent attribute of a signal. When thinking theoretically, you're in the habit of defining some t=0, which will define what is negative and what is positive. Negative and positive frequencies have physical significance only in a process that already includes a FFT function with a defined timing (a defined t=0 which has some physical meaning, like when the FFT circuit is reset). In an actual circuit you would need to "reset" the FFT process at some point in order to define a t=0, if you want frequency polarity to have physical meaning. And once you do all that, you've got a frequency-domain signal that makes it easy to remove the negative frequencies, anyway. Then do a IFFT. There's no shortcut to doing a FT, since FT, by definition, means "getting the frequency components of a time domain signal" (although admittedly *how* one gets the frequency components is up for efficiency improvements). Certainly there would be a minor (probably insignificant) simplification of a standard FFT circuit/algorithm when all you wanted was the positive frequencies.

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sophiecentaur

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Warren, Are you saying there is no physical significance attached to negative frequencies?

"Physical significance"?

The spectrum is just a mathematical way of describing things. Sometimes, the maths suggests the presence of signals but you can't necessarily measure them. This is only like saying that you want a 'Physical Significance' for one of the roots of a (mathematical) equation of motion which doesn't fit the physical problem. You just have to pick the more 'suitable' result.

Try this link to see a thread which touches on just this topic.

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Sophie, I get that we have been 'picking the more suitable result' for analysing the signal. But, I recently read a paper titled "Negative frequency communication" which says that half of the frequency(negetive) is being wasted and it does have a physical meaning. You can read more about it here-"Physical significance"?

The spectrum is just a mathematical way of describing things. Sometimes, the maths suggests the presence of signals but you can't necessarily measure them. This is only like saying that you want a 'Physical Significance' for one of the roots of a (mathematical) equation of motion which doesn't fit the physical problem. You just have to pick the more 'suitable' result.

Try this link to see a thread which touches on just this topic.

http://arxiv.org/abs/1012.1403

so is it just a mathematical eventuality or is there more meaning to it??

- #14

sophiecentaur

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People have used 'independent sideband' transmissions and suppressed the carrier.

I may be doing the author a disservice here but it certainly looks like that to me. I would need access to the whole paper but I can't seem to find it.

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I've read the whole paper. Its not about SSB modulation. The author specifically talks about using the negetive frequency components for communication. Heres the link to the paper-

People have used 'independent sideband' transmissions and suppressed the carrier.

I may be doing the author a disservice here but it certainly looks like that to me. I would need access to the whole paper but I can't seem to find it.

http://arxiv.org/pdf/1012.1403v5.pdf

Any feedback would be appreciated.

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Well there is no such thing as negative frequency. In real life. That doesn't make sense.

I only think math behind the fourier transform, and generally math tools are made in that way so that we do operate with negative frequencies.

Cosine is represented with 2 deltas right? (amplitude spectra)

Eliminate one of them, and you no longer have a cosine...

Specifically lets consider this.

[itex] F (cos(\omega _0 t)) = \pi\left[\delta (\omega -\omega _0)+\delta (\omega +\omega _0)\right] [/itex]

Eliminate the negative frequency and you get:

[itex]\pi\left[ \delta (\omega -\omega _0)\right][/itex]

Inverse Fourier transform of this is no longer a cosine. Its complex exponential:

[itex] F^{-1}(\pi\left[ \delta (\omega -\omega _0)\right])=\frac{1}{2}\cdot e^{j\omega _0 t}[/itex]

So its not even a real function anymore.

You can go with using a complex exponential as your carrier.

Design a system, which transfers in parallel a Sine and a Cosine.

I only think math behind the fourier transform, and generally math tools are made in that way so that we do operate with negative frequencies.

Cosine is represented with 2 deltas right? (amplitude spectra)

Eliminate one of them, and you no longer have a cosine...

Specifically lets consider this.

[itex] F (cos(\omega _0 t)) = \pi\left[\delta (\omega -\omega _0)+\delta (\omega +\omega _0)\right] [/itex]

Eliminate the negative frequency and you get:

[itex]\pi\left[ \delta (\omega -\omega _0)\right][/itex]

Inverse Fourier transform of this is no longer a cosine. Its complex exponential:

[itex] F^{-1}(\pi\left[ \delta (\omega -\omega _0)\right])=\frac{1}{2}\cdot e^{j\omega _0 t}[/itex]

So its not even a real function anymore.

You can go with using a complex exponential as your carrier.

Design a system, which transfers in parallel a Sine and a Cosine.

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- #17

sophiecentaur

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If you consider the actual Power involved in his proposed system, if it were anything other than some version of this, then (up to) 100% excess power would have to come from somewhere in the transmitter if information were to be available at the other end of the link by way of this extra available channel.

Using two polarisations for two transmitting channels is, again, nothing new. Every TV transmitter network uses polarisation diversity in its service planning.

This seems to me like a good bit of theoretical bookwork that has been done in a bit of a vacuum. He cites no RF Engineering references to put the work in a real world context and I wonder whether he is actually aware that he may well be re-inventing a wheel.

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http://pokit.org/get/1ce09bbe329cdfd1847282b373f7d3ac.jpg [Broken]

Method using sine and cosine as carrier.

http://pokit.org/get/41a7f4cf9f65ff190857c955c0b3712d.jpg [Broken]

Frequency spectra.

Full link:

http://ocw.mit.edu/resources/res-6-...ous-time-modulation/MITRES_6_007S11_lec13.pdf

Method using sine and cosine as carrier.

http://pokit.org/get/41a7f4cf9f65ff190857c955c0b3712d.jpg [Broken]

Frequency spectra.

Full link:

http://ocw.mit.edu/resources/res-6-...ous-time-modulation/MITRES_6_007S11_lec13.pdf

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- #19

sophiecentaur

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Hang on a minute. How would you combine your two signals losslessly from two high power amplifiers? I think that could be a problem.

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I only know the theory behind it, I never designed one :D

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Bassalisk, How do i go about generating the complex exponential e^(jwt)? You said a system which transfers sine and cosine waves in parallel. Do you mean sin(wt)+cos(wt)? shouldnt it be cos(wt)+j sin (wt)?Well there is no such thing as negative frequency. In real life. That doesn't make sense.

I only think math behind the fourier transform, and generally math tools are made in that way so that we do operate with negative frequencies.

Cosine is represented with 2 deltas right? (amplitude spectra)

Eliminate one of them, and you no longer have a cosine...

Specifically lets consider this.

[itex] F (cos(\omega _0 t)) = \pi\left[\delta (\omega -\omega _0)+\delta (\omega +\omega _0)\right] [/itex]

Eliminate the negative frequency and you get:

[itex]\pi\left[ \delta (\omega -\omega _0)\right][/itex]

Inverse Fourier transform of this is no longer a cosine. Its complex exponential:

[itex] F^{-1}(\pi\left[ \delta (\omega -\omega _0)\right])=\frac{1}{2}\cdot e^{j\omega _0 t}[/itex]

So its not even a real function anymore.

You can go with using a complex exponential as your carrier.

Design a system, which transfers in parallel a Sine and a Cosine.

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Bassalisk, How do i go about generating the complex exponential e^(jwt)? You said a system which transfers sine and cosine waves in parallel. Do you mean sin(wt)+cos(wt)? shouldnt it be cos(wt)+j sin (wt)?

There wouldn't be imaginary current or potential in an actual circuit. The circuit depicted carries two separate products with sine and cosine waves respectively, to represent multiplying by a complex exponential.

You should know that real signals have Hermitian symmetry in the frequency domain. The component at a negative frequency is the complex conjugate of the component at the corresponding positive frequency.

This has to do with the symmetry of cosine and the "odd" symmetry of sine. Consider what happens if we make the frequency negative.

cos(ωt) = cos(-ωt)

but

sin(ωt) = -sin(-ωt)

Anyway, removing the negative frequencies seemingly would imply two outputs instead of one, based on Hermitian symmetry requirement for the frequency domain of real signals.

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Bassalisk, How do i go about generating the complex exponential e^(jwt)? You said a system which transfers sine and cosine waves in parallel. Do you mean sin(wt)+cos(wt)? shouldnt it be cos(wt)+j sin (wt)?

Well, imaginary numbers are a pair of real numbers. So that system that I posted in the post above, explains it nicely.

When you go deeper into Signals and Systems, these things are pretty easy to understand :D

- #24

sophiecentaur

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I think you can do the analysis (albeit in a more lumpy way) without using i at all.

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I think we are confusing real, time varying signals with a convenient mathematical representation of them. Neither the exponential notation or the 'cis' notation are any more than models, and 'half' of that model is not relevant to the real world. afaik, one should really prefix the final result of any 'complex' jiggery pokery with the words "The Real Part Of . . . " if you want to get a proper answer.

Well put.

- #26

sophiecentaur

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That's where that paper on "negative Frequencies in Modulation" seems to be skating on thin ice.

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That's where that paper on "negative Frequencies in Modulation" seems to be skating on thin ice.

Yes its somewhat like talking about negative time. But nevertheless, this thread was really interesting!

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So, is x(t)cos(wt)+y(t)sin(wt) the required complex exponential modulated signal?Well, imaginary numbers are a pair of real numbers. So that system that I posted in the post above, explains it nicely.

When you go deeper into Signals and Systems, these things are pretty easy to understand :D

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So, is x(t)cos(wt)+y(t)sin(wt) the required complex exponential modulated signal?

x(t)cos(wt)+j*x(t)sin(wt) ****

y(t) would have a real part x(t)cos(wt)

y(t) would have an imaginary part x(t)sin(wt)

They come in pairs.

http://ocw.mit.edu/resources/res-6-...ctures/lecture-13-continuous-time-modulation/

This video is very much addressing that subject.

- #30

sophiecentaur

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Why look for anything more significant when some Maths suggests that a Negative Frequency component could exist for a signal? At the beginning of the thread there was a question about the existence of Power in this 'Mirror' signal. Clearly not. A square wave oscillator takes power from its (DC) power supply (real, measurable Joules from a battery). This Power is exactly the same as the power in the square wave - as you can see by heating up an element or by integration. There is no other power in the system. The 'negative frequency' component is just an artifact of the Maths - just like the negatively dimensioned carpet. The same applies to a sinewave.

So what about the two sidebands which are generated in AM? They are at (absolute) positive frequencies and carry energy - along with the carrier and, if you add up the three Powers, you get the value of Power which the power supply delivers (less a measurable / calculable factor due to the efficiency of the modulator. The power in each sideband can be used to carry other information and the power of the carrier can be reduced to zero - giving you two SSB transmissions, each of which has the same SNR as the original dsbam signal, half the signal spectrum occupancy and

When you draw diagrams of signal spectra and show them shifting around and being filtered, there is no explicit mention of the Power involved. So the diagram proves nothing about the existence or otherwise of 'components'.

I, personally, was a bit disappointed with that MIT Movie. It would be very easy to get some wrong messages from it, I think. OK, as far as it went but strictly an undergraduate treatment of the topic, I should say, aimed at getting predictable results from a comms system.

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