Talk:In-phase and quadrature components

Why the term quadrature
One thing I was hoping this article would answer for me as a reader is why the 90 deg out of phase component is called the quadrature phase? What is the relation between 90 deg out of phase and quadrature. the only thing that comes to my mind is that the two components span a two-dimensional parameter space (the complex plane) and a quadrature relates to squaring, which you do to get an area in two dimensions... -- Slaunger (talk) 14:43, 26 May 2008 (UTC)
 * I think it is simply defined this way - does anyone have a better explanation (ie. this 2D space explanation?) daviddoria (talk) 12:29, 15 September 2008 (UTC)

The term quadrature comes from the fact that the quadrature is 90 degrees (i.e., one-fourth of a circle) out of phase with the in-phase signal. The "quad" comes from the one-fourth. 271828e (talk) 21:23, 5 February 2010 (UTC)

This article should be able to be understood by an audience of those who actually work with technology that utilizes the concept (e.g., DSL technical support) but may have no formal technical training in it. 69.140.152.55 (talk) 14:38, 5 August 2008 (UTC)

General definition
I suggest that this article should be made more general, under this or a revised heading. I found this definition using a search engine:

Quadrature (electricity). "A vector representing an alternating quantity which is in quadrature (at 90°) with some reference vector. reactive component." []

As an example we could say something like:

e.g. the alternating current in a pure reactance (inductor or capacitor) is in phase quadrature (lagging or leading respectively) the applied alternating voltage.

Or something. Any suggestions? GilesW (talk) 22:52, 10 April 2009 (UTC)

Shouldn't this be moved to the AM, FM or PM pages, and included there? Why is this a separate topic? At least there should be links to the others (to aid in understanding). 271828e (talk) 21:24, 5 February 2010 (UTC)

New introduction
The new intro (Oct 22) is an improvement, for EE circuit folks, but it is too EE-ish, too remedial in places, unsourced, and for its tedious length, it doesn't shed much light on the reasons for IQ. I have composed a more general, sourced intro, which I will install, and we can go from there. I also simplified the communication example formula, because the amplitude factor, A(t), unnecessarily obfuscates the IQ concept. --Bob K (talk) 14:54, 25 October 2013 (UTC)

Angle Modulation
The article states: While technically true, I believe this is misleading - I-Q mod can be used to synthesize any signal which is angle modulated, amplitude modulated, or a combination thereof. That's why it's so popular in SDR transceivers. Would anybody object if I made this change? - Freyyr890 07:16, 31 March 2014 (UTC) — Preceding unsigned comment added by Freyyr890 (talk • contribs)
 * In electrical engineering, a sinusoid with angle modulation can be decomposed into, or synthesized from, two amplitude-modulated sinusoids that are offset in phase by one-quarter cycle (π/2 radians).


 * My concern is that we don't obfuscate the "interesting" point with mundane detail. For instance, at In-phase_and_quadrature_components, we start with:


 * $$\sin[2\pi ft + \phi(t)]\ =\ \sin(2\pi ft)\cdot \cos[\phi(t)] +\ \sin\left(2\pi ft + \tfrac{\pi}{2} \right)\cdot \sin[\phi(t)],$$


 * which is much more interesting than the minor detail (mentioned later) that both sides can be multiplied by A(t).
 * --Bob K (talk) 12:55, 31 March 2014 (UTC)

Concept
The switcheroo from $$\varphi'$$ to $$\phi$$ at the very end comes across like sleight of hand. And from a communication engineering pov, it isn't helpful to focus on the two different decompositions of one waveform. It's more useful to focus on the similarities between two different waveforms, caused by a phase-shift. --Bob K (talk) 17:29, 25 May 2018 (UTC)
 * - The switcheroo and sleight of hand is the standard method of expressing an arbitrary value $$\phi$$ from some domain that takes on two specific, different values $$\varphi$$ and $$\varphi'$$ in two different representations ($$\sin$$ or $$\cos$$), of one specific sinusoid, a carrier wave; and this without abuse of notation. Abuse of notation may be very familiar, and does not generate misunderstandings (not anymore) within those, who are used to it, but establish a massive burden for anyone new to the subject.
 * - Throughout your revision of my edits you removed hints to the general meaning of the employed terms. It starts with the expendable coordinates, but goes on to remove context of the important general notion of orthogonality that is inherently independent of the selection of a basis, i.e., coordinates. A slight hint what orthogonality, amongst other things, is good for: –power–, has been removed, thus leaving the notion orthogonality of functions from functional analysis almost without any physical (signal theoretical) background.
 * - It is obviously untrue that the components of a vector do not change when the basis changes, and vice versa. The products of a specific decomposition do change if the decomposed object changes. Using $$\varphi$$ and $$\varphi'$$ makes this reasonably accessible.
 * - Finally, I think that numbering equations as just 1 and 2, with only one reference, is notational overkill.
 * I intend, if you don't want to discuss specific items here on the TP, to suggest my version, with special regard to your intentions, directly in the article within a few (3?) days. Best regards, Purgy (talk) 12:41, 26 May 2018 (UTC)

If you want to hint at what orthogonality is good for, in the context of communication engineering, demodulation would be more useful than power. I numbered the 2nd formula on the assumption that there may be more iterations, and the number might come in handy. --Bob K (talk) 16:03, 26 May 2018 (UTC)


 * Could you, please, provide your view on the primary connection of orthogonality to demodulation? I am a dilettante in signal theory, and my access to this is via efficiently separating maxima in the power spectrum, so again would primarily involve power, which is to me, because of its quadrature provenance, near to the integral definition of orthogonality. Purgy (talk) 10:28, 27 May 2018 (UTC)

Also see Quadrature_amplitude_modulation. Briefly, a common task is to extract the low frequency modulation (thick red and blue lines) separately. The low-pass filtered product of cos(wt+φ) and cos(wt) produces cos(φ), and the product of cos(wt+φ) and cos(wt+π/2) produces sin(φ). The utility of this is that cos(φ) and sin(φ) can be independently generated baseband signals. I.e. they are not determined from a common φ; rather φ is defined by two independent functions. --Bob K (talk) 13:47, 27 May 2018 (UTC)
 * On second thought, I better do not interfere with this article for the time being. Purgy (talk) 06:44, 28 May 2018 (UTC)

I agree. Thanks so much for your self-awareness. --Bob K (talk) 20:05, 28 May 2018 (UTC)


 * Thanks for the warm good riddance by a true sage. Purgy (talk) 05:53, 29 May 2018 (UTC)

graph caption
Hi. The graph on the top of the article has 5 lines (signals) but only 2 are identified in the caption. Can someone be more verbose on this.

Also I propose the caption will only discuss one "decomposing" and add a last sentence saying it's the same for "synthesized".

I imagine it would make the topic clearer. Kotz (talk) 07:47, 3 January 2019 (UTC)

Franks and AM
The questioned statement is In some contexts it is more convenient to refer to only the amplitude modulation itself by those terms. citing Franks Signal Theory (1969) p.82. But on examination of that source, the text there doesn't seem to support the statement. Is there some explanation that may help? Chumpih t 17:26, 12 February 2023 (UTC)


 * What is it about the sentence "The real lowpass signals u and v are called the in-phase and quadrature components, respectively, of the bandpass signal." that doesn't support the statement?
 * --Bob K (talk) 19:19, 12 February 2023 (UTC)


 * The 'u and v' suggests an amplitude+phase modulation. Amplitude-onlhy modulation would come under Single side band (SSB-AM, perhaps MSB, USB) and doesn't necessarily use IQ.  Per Franks that would be on p.88 - and somewhat different to IQ.  Chumpih  t 19:48, 12 February 2023 (UTC)


 * I hope you're not trolling me. But you clearly don't understand the graphic image.  Have you even tried?  $$\cos(\phi(t))$$ is amplitude modulating $$\cos(2\pi ft),$$ and $$\sin(\phi(t))$$ is amplitude modulating $$\cos(2\pi ft + \pi/2).$$
 * --Bob K (talk) 20:14, 12 February 2023 (UTC)


 * Ah, perhaps there is some confusion due to the tautological nature of Such amplitude modulated sinusoids are known as the in-phase and quadrature components. In some contexts it is more convenient to refer to only the amplitude modulation itself by those terms. What does the second sentence here bring that the first doesn't already state? It might be easy to think that 'amplitude modulation only' refers to AM.  That's the issue.  Can there be another form of the sentences that is less prone to misinterpretation?  Chumpih  t 20:33, 12 February 2023 (UTC)


 * Seriously?? The first sentence means (in our example) the I component is $$\cos(2\pi ft)\cos(\phi(t)),$$ and the 2nd one means the I component is just $$\cos(\phi(t)).$$
 * --Bob K (talk) 20:43, 12 February 2023 (UTC)
 * Right, I get what you're saying. Thanks for the explanations, and apologies that it took so long for me to understand.  So how about something like Such amplitude modulated sinusoids are known as the in-phase and quadrature components. In some contexts it is more convenient to refer to only the amplitude modulations themselves by those terms, i.e. I and Q may refer to the values that would multiply the sinusoids, not the full waveforms, e.g. in the term "a stream of IQ data". ?  Chumpih  t 20:51, 12 February 2023 (UTC)


 * I'm glad we persevered. But I don't think the distinction is important enough to warrant the extra verbiage.  Its only purpose is to help settle potential semantic disputes.  Most readers won't be worrying about the exact semantics.
 * --Bob K (talk) 00:00, 13 February 2023 (UTC)
 * Genuinely, the extra verbiage brings some clarity. Without, there is demonstrable risk of misunderstanding.  Chumpih  t 04:53, 13 February 2023 (UTC)


 * Good afternoon. I still think the sentence is sufficient.  I can't be inside your head, but I think you read it with a preconceived opinion that there is only one universal semantic, so there must be something wrong with the message rather than with your preconception.  But it has been like that for about 10 years, and you are the first to want a more pedantic explanation.  Others either re-read more carefully or continue on with their own preconception, which is really OK.  It doesn't really matter until you get into a debate with someone else's different preconception.  Then they can come here and find out that they are both right.
 * If you are still insistent, let's compose a footnote.


 * A more serious nitpick, BTW, is the first two paragraphs. In paragraph 1, the phrase "shows how much" is not valid.  And in paragraph 2, the inline use of "e.g." is not encyclopedic, and (in my opinion) the 1st and 2nd sentences are not as related as the word "therefore" implies.
 * --Bob K (talk) 18:27, 13 February 2023 (UTC)
 * Do please go ahead and edit! I still feel the clarification suggested (or something like it) would be beneficial.  At the very least, state components' amplitude modulations themselves ....  Chumpih  t 19:06, 13 February 2023 (UTC)


 * OK, so I did. I used your 12-Feb (oldid=1138888574) version as a basis, but re-ordered differently.  I think you will find your stuff still there.  And keep in mind that we don't have to repeat a lot of the information at the WikiLinks... it's what they're  for.
 * --Bob K (talk) 21:11, 13 February 2023 (UTC)
 * Have re-tweaked a little to remove a few potential ambiguities. the version you cited went through several further revisions.  Chumpih  t 23:29, 13 February 2023 (UTC)


 * A couple of problems:

A typical application is quadrature amplitude modulation, where two independent data-streams provide the relatively low-frequency (baseband) amplitude modulations, which are also sometimes known as the I and Q components. (also see ) Re. the different form of words, QAM is an example of a modulation scheme, and IQ works across many modulation schemes including QAM. Also (as previously stated) Franks doesn't include the word baseband, nor does p.82 include information on the data rate of the IQ stream, so as a reference to support the preceding sentence it is suboptimal. I and Q components is already writ large, so with all that, there's not much left to justify the sentence. Well, IMHO. Chumpih t 18:06, 14 February 2023 (UTC)
 * The decomposition also has relevance within. Actually, no.  The actual purpose of that section is to show the difference between quadrature components of one signal vs two distinct sinusoids (e.g. voltage and current) that are in phase quadrature, but can have different amplitudes, different units, and even exist on different circuits.
 * Why did you remove
 * --Bob K (talk) 13:27, 14 February 2023 (UTC)
 * Re. the AC, 'relevance' may be the appropriate word, but if you think not, by all means put something better there.


 * The Franks citation needs to be there to "officially" justify the statement that I and Q are used in both baseband and RF contexts. That's all.  It's not there to support data-rate claims.  And it doesn't have to use the word "baseband".  A paragraph reference doesn't have to include every detail contained in the paragraph.
 * --Bob K (talk) 00:32, 15 February 2023 (UTC)
 * In the sentence we're discussing that got removed, it starts with a typical application is QAM, where.... so the reader could go on to presume that the rest of the sentence is in the context of QAM alone, which is unhelpful. The removed sentence states two independent data-streams provide the relatively low-frequency (baseband) amplitude modulations when they are not independent by many meanings of that word, they are very much related. Franks is an out-of-print book, so isn't an easily-checked source for any statement, and there are so many others.
 * The upshot being that there is arguably sufficient issues with the sentence to warrant another form.
 * You make an excellent point in that we should justify our statements with sources. I'll do some of that now.  Chumpih  t 05:39, 15 February 2023 (UTC)


 * First of all I'm not aware of any WP policy against out-of-print citations. And citations are not mutually exclusive.  So feel free to add your own favorites, but leave mine alone.  If I like what you come up with enough, I might remove my own citation.
 * Nitpick: I still object to The decomposition also has relevance within...(etc).  The point of that section is that it really isn't relevant.  As a compromise, I added a  template to the header.
 * --Bob K (talk) 13:30, 15 February 2023 (UTC)
 * You're right re. decomposition has relevance. I've deleted that.  Chumpih  t 06:23, 18 February 2023 (UTC)