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Table of standard symbols

I think we should standardize the use of symbols, notation, and terminology as much as possible across all electronics-related articles. -- Rdrosson 02:27, 20 October 2005 (UTC)

Table moved to project page for visibility & comments by wider audience--Light current 16:09, 21 November 2005 (UTC)

Well I agree with all the above except, guess which? Yes, I really think damping factor should be zeta, its used in all the books and texts I have and is universally understood.--Light current 11:23, 20 October 2005 (UTC)

The idea of the table of standard symbol is alright: just wait for a while and then add it to the main article. About the damping factor, according to its definition, it is defined as the ratio between two loads. Since the universal symbol for a generic load is Z, it would be confusing to use the same symbol for something different. In the Damping factor article DF is used, that looks alright. Alessio Damato 13:30, 20 October 2005 (UTC)

Please be careful here. There are two sorts of damping factor. Im talking about the one measured in rad/sec. (not the ratio of 2 loads)--Light current 14:15, 20 October 2005 (UTC)

do you think the table is ready for the main page?? I think we might do as we did for the programs: we create its own page and then we link it on the main page. Alessio Damato 18:40, 15 November 2005 (UTC)

Yes I think the table of symbols could now go on the main page and be accepted as policy, unless someone objects. We should get more comments anyway if its on our front page! I would leave it on the main page a few weeks for comments before giving it its own sub page.

--Light current 21:59, 15 November 2005 (UTC)

Please have a look at Electromagnetism#SI_electricity_units before u start the changes. --Electron Kid 20:48, 14 December 2005 (UTC)

The imaginary unit

The imaginary unit is $\ j\$ in network theory but, is really $\ i\$ in mathematics theory. Also, take special care of vector quantities. --Davy Jones 02:30, 23 October 2005 (UTC)

Yes I think we should use j for the imaginary operator. i can be confused with current!--Light current 01:31, 30 October 2005 (UTC)

j is the standard symbol for -1^1/2 in electronics, no question about it. Snafflekid 04:17, 28 October 2005 (UTC)

This has already been discussed elsewhere, and j should be used in electronics articles. — Omegatron 05:07, 28 October 2005 (UTC)

Current symbols

There is a difference between I for DC current and i for ac current. Also, while taking Laplace transformation of circuits, the initial consideration is of i(t) and then we convert it to I(s). Also, we cant just go by using symbols that confuse; don't we need to check the rules? Ilso, to limit page size and to make it look more professional, how about writing the dimensions as dimensions instead of the word form and make a separate column for SI units and dimensions? --Electron Kid 00:53, 30 October 2005 (UTC)

It depends on what the goal is. If the goal is to help explain these concepts to people who are struggling to understand them, then it seems to me that we would want to spell things out as much as possible. If the goal is to write a bunch of technical mumbo-jumbo that only engineers and Ph.D. mathematicians can understand, then I think we should try to use the most arcane and obscure abbreviations possible. -- Rdrosson 03:28, 2 November 2005 (UTC)

It is not the matter of PhD/PhDs. thanks. But try atleast for vector and scalar quantities. --Electron Kid 02:06, 30 November 2005 (UTC)

Changing ohm to Ω

I'm writing some regular expression things to automatically fix units, and I'm wondering if anyone has a problem with converting:

• (number) ohms → (number) Ω
• (number) (SI prefix)ohm → (number) (SI prefix)Ω

In other words, any occurrence of "kohm" will become "kΩ", "5 ohms" will become "5 Ω", and so on. Can you think of any situations where "ohm" would be superior? It won't change words like kiloohm. — Omegatron 22:30, 22 October 2005 (UTC)

Sounds great to me, kohm is incorrect terminology, but kiloohm is correct. If you are creating a bot, you should check Wikipedia:Bots FYI Snafflekid 22:41, 22 October 2005 (UTC)

It's not a bot, really. It's a custom tab that fixes a bunch of stuff in one go and then I press "show changes". Here's an example diff of the things it fixes: [1] (and the other things on the page were not changed). — Omegatron 00:55, 23 October 2005 (UTC)

Should it not be kilohm? (only one o. or should it have a hyphen?) A bit like Ammeter instead of Ampmeter(but different)--Light current 23:34, 22 October 2005 (UTC)

Either is valid, as explained in the ohm article. — Omegatron 00:55, 23 October 2005 (UTC)

Should that be k or K in kilo and similarly for others? I think capitals are for 10^+ve and small caps for 10^-ve.--Electron Kid 13:35, 30 October 2005 (UTC)

No. k is lowercase. See SI prefix. Good point, though. That would make more sense.

"There are also proposals for further harmonization of the capitalisation. Therefore the symbols for deka, hecto and kilo would be changed from "da", "h" and "k" to "D" or "Da", "H" and "K" respectively. Likewise some lobby for the removal of prefixes that don't fit the 10^±3·n scheme, namely hecto, deka, deci and centi. The CGPM has postponed its decision on both matters for now." — Omegatron 16:58, 30 October 2005 (UTC)

Don't change "ohm" to the Greek letter &Omega - it's very common for computers to render the letter incorrectly, leading to one on-line catalog showing things like 100 W 1 W resistors - 100 ohm 1 watt? 100 Watt 1 Ohm? --Wtshymanski 20:41, 15 November 2005 (UTC)

Yeah, I think I've been to that catalog, and wrote them a note about it. :-) There's a difference between the character I'm using: Ω and the ugly method they were using that only works on IE: W. — Omegatron 20:58, 15 November 2005 (UTC)

weighting filters

Can some other people comment on whether weighting filter should cover any old type of weighting, whether the audio weighting filters should get their own article, or whether A-weighting should be separated from the other audio weightings? See Talk:weighting filter and Talk:A-weighting. — Omegatron 05:59, 28 October 2005 (UTC)

I have no strong feelings on this subject, but I think that 'weighting' is maybe more commonly used for audio purposes than for anything else. So IMHO article should be called 'audio weighting filters' and include A weighting filter. Other weigthing filters can be mentioned at the end of the article or linked to if there ar other articles about 'weighting filters' being used in non-audio applications.--Light current 17:41, 29 October 2005 (UTC)

I'll weigh in. From what I know and have read weighing deals with adapting a signal to the human acoustic and visual system. Most recording systems are able to detect frequencies linearly but ears and eyes are non-linear. That's what I know. A-weighting is not the only commonly used filter, μ-weighting is common in telephony. Audio weighting is definitely large enough to be its own page and audio is the major application of weighted filters. Snafflekid 18:24, 29 October 2005 (UTC)

I don't agree. Weighting is a general scientific term,used in statistics and epidemiology. There are many weighting curves used in telephony (psophometric P53 etc, telephone instrument weightings etc). Audio may be the most common use, but A-weighting is not the most commonly used curve: ITU-R 468 dominates the broadcast and professional markets outside the US. I'm against the narrowing of meanings, and would rather see unlimited specialist pages forming a tree of knowledge, starting from a 'root'page which introduces the field, leaving it open for all to add to. Weighting is used in areas as unusual as UV weighting for sunburn skin damage. --Lindosland 14:10, 9 December 2005 (UTC)

Yes, well were only dealing with electronics on this project as yet and in fact the page title isweighting filters. You would need to get a very broad consensus to implement your ideas.--Light current 14:35, 9 December 2005 (UTC)

drawing circuits 2

why was the drawing circuits section moved to the talk page?? we didn't talk about it. I think it should remain on the main page, as long as we take a firm decision. Alessio Damato 21:21, 2 November 2005 (UTC)

I don't think there's really a decision to make. It's just a list of information that would be useful. Until a perfect program comes around with all the features we want, I guess we're just choosing on a case-by-case basis? — Omegatron 21:24, 2 November 2005 (UTC)

exactly, so why shouldn't it be on the main page? at least it could be moved to a dedicated page. The talk is not the place for it, since here we should have things to talk about, while that part about programmes is, as you called it, a list of useful information. Reading that, anyone may decide to use a specific programme. Tell me what you think about it; if nobody is against that, I'll make a dedicated page soon. Alessio Damato 00:18, 3 November 2005 (UTC)

Yes, put it on its own page. It was tending to dominate the main page- thats why I moved it--Light current 23:30, 3 November 2005 (UTC)

Where is everything??

There used to be all kinds of info on this page. Why was it removed? — Omegatron 02:23, 6 November 2005 (UTC)

Ive only moved the stuff about drawing systems to talk. To what else are you referring?--Light current 02:27, 6 November 2005 (UTC)

Ahh perhaps you need to refer to Archive1!--Light current 02:29, 6 November 2005 (UTC)

Signals and LTI System Theory

because the Digital Communications wikiproject does not seem as active as this one, i am bringing this up here.

i am greatly disappointed in nearly all of the articles LTI System Theory and DSP fundamentals. there are several problems, but the overall problem is that they seem to be written by grad students in EE or mathematics (seem to be often from the UK, judging from the style) and are written in such a way that the goal is to impress with mathematical lingo (functional analysis, etc.) and not to introduce a person less schooled in the art to what the topic really is about.

notation between articles is often inconsistent. i hate the fact that the Fourier Transform and inverses are only portrayed with angular frequency, so there are scaling factors of $2\pi \$ all over the place. it's just ugly.

this is where the discussion of topics such as what really makes a Butterworth Filter (what are the properties of 2^nd order filters, etc.) should be. where the poles and zeros go to make the filter do what you want it to.

i'm wondering if there should be a related wikiproject for LTI System Theory and Signal Processing, where a bunch of editors can get together and start ironing this stuff out. r b-j 16:34, 29 November 2005 (UTC)

I believe we have a number of signal processing ?experts? already on this project, so perhaps it would be a good idea to keep the discussion here for the moment. If it expands greatly, then we can always hive it off!

BTW ther seems to be some missing text in your last post!

--Light current 17:05, 29 November 2005 (UTC)

i tried to fix incomplete sentences, etc. sometimes i don't make myself clear, either.

i dunno how i stack up against the other signal processing experts on this project, but i invite anyone to google me (also google groups) and decide for yourself. my professional emphasis is audio, but my concern here is simply more general. i'll bring up some concerns right here as i can recall them:

1. We should recognize that all of these signal processing and system theory articles, as well as descending disciplines such as digital or analog communication theory, information theory, control theory, electrical and electronic circuits, filter design, instrumentation, transmission lines (or sometimes called "distributed networks") as well as antenna theory (steered arrays, etc.), DSP of course, and even more ancillary fields such as audio signal processing and electronic and computer music, speech processing, biomedical, whatever, that these are fields that fall (in whole or in part) under the larger electrical engineering discipline. That means the language and symbols should be consistent under that discipline.

2. The symbol for the imaginary unit should always be $j\$ and never $i\$ (but we must recognize where the topic of an article has a broader mathematical interest and is not just for EEs, then we should let them define it as $i\$).

3. In the continuous time domain, symbols for voltage should always be $v(t)\$, current $i(t)\$, a generic output should usually be $y(t)\$, inputs usually $x(t)\$ (except in control theory where state variables are $x_{m}(t)\$ or $\mathbf {x} (t)\$ in the lit, sometimes they use $u(t)\$ for input which, I know, is also used for the unit step function), impulse responses are $h(t)\$ or sometimes $g(t)\$, window functions are $w(t)\$, error signals $e(t)\$ (or possibly $q(t)\$ for quantization error), all possibly subscripted to differentiate one quantity from another like quantity. In the case where other letters are needed (because they are commonly used in the lit or are elegant to use), they should all be small case for signals in the time domain. We should normally not have $s(t)\$ (because of confusion with the Laplace transform variable $s\$) nor $z(t)\$ (because of Z transform) nor ever use $f(t)\$ unless it represents a (time variant) frequency signal or parameter.

4. In the Laplace frequency domain, symbols for voltage should always be $V(s)\$, current $I(s)\$, a generic output should usually be $Y(s)\$, inputs usually $X(s)\$ (except in control theory where state variables are $X_{m}(s)\$ or $\mathbf {X} (s)\$ in the lit), transfer functions are $H(s)\$ or sometimes $G(s)\$, all possibly subscripted to differentiate one quantity from another like quantity.

5. The continuous-time Fourier transform and inverse should most often be defined as:

$X(f)=\int _{-\infty }^{\infty }x(t)\,e^{-j2\pi ft}\,dt\$

$x(t)\equiv \int _{-\infty }^{\infty }X(f)\,e^{+j2\pi ft}\,df\$

because with that symmetry of definition (now used often in communications texts), the use of the Duality theorem and Parseval's theorem (as well as the DC value vs. integral of transformed function theorem) are trivial. No crappy scaling factors to remember and worry about (which are used in only one direction). Also transforms of rectangular pulses, sinc functions, gaussian pulses, and chirp functions are trivial. In the cases where we never need a complex frequency argument (as in Laplace), this definition of Fourier transform is, nearly every time, superior in elegance and compactness of expression and manipulation. When the Fourier transform is used as such, we should indicate that in the article (so the reader knows not to simply substitute $s\$ or $\omega \$ for $f\$ without some scaling. (And a section should be put in the article Fourier transform to include this definition.)

In the cases were the angular frequency version of the Fourier transform is perferable, we should have the Fourier Transform strictly compatible with the common double-sided Laplace transform definition:

$X(j\omega )=\int _{-\infty }^{\infty }x(t)\,e^{-j\omega t}\,dt\$

$x(t)\equiv {\frac {1}{2\pi }}\int _{-\infty }^{\infty }X(j\omega )\,e^{+j\omega t}\,d\omega \$

Here, in this case, one can directly equate $s\$ to $j\omega \$ as a generalizing case or the other direction as a degenerate case. But we should see $X(j\omega )\$ in the angular frequency case and never see $X(\omega )\$. If the argument is purely real, it should be the "Hertz" convention: $X(f)\$ not angular frequency radian/sec.

6. All discrete-time signals should be just like their continuous-time counterparts except brackets used in lieu of parenths and an integer-like symbol (e.g. $n\ k\ m$ perhaps $l\$ and only $i\$ if we run out) for the discrete-time argument. That is, inputs are usually $x[n]\$ (except in control theory where state variables are $x_{m}[n]\$ or $\mathbf {x} [n]\$ in the lit), impulse responses are $h[n]\$ or less commonly $g[n]\$, window functions are $w[n]\$, error signals $e[n]\$ (or possibly $q[n]\$ for quantization error), all possibly subscripted to differentiate one quantity from another like quantity. The discrete-time index variable should never be a subscripted symbol!!! And the discrete-time index variable should always be inside of brackets, not parenths unless it becomes an argument in a continuous-"time" function. At least, not in this electrical engineering context.

7. Discrete-frequency functions should look like the discrete-time counterparts except large-case letters used for the function (brackets rather than subscript and an "interger-like" letter such as $n\ k\ m$ used for discrete frequency). The DFT would look like:

$X[k]=\sum _{n=0}^{N-1}x[n]e^{-j2\pi {\frac {nk}{N}}}\$

$x[n]\equiv {\frac {1}{N}}\sum _{k=0}^{N-1}X[k]e^{+j2\pi {\frac {nk}{N}}}\$

Again subscripting would be used to differentiate one discrete-frequency function from another like quantity, but would not be used as the discrete-frequency index.

8. In discrete-time contexts we would make sure the article says that $X(z)\$ is the Z transform of $x[n]\$ and not the Laplace transform with $z\$ substituted for $s\$ or the Fourier transform with $z\$ substituted for $f\$. I think we should always use the double-sided Z transform definition:

$X(z)=Z\{x[n]\}=\sum _{n=-\infty }^{\infty }x[n]z^{-n}\$

$x[n]=Z^{-1}\{(X(z)\}={\frac {1}{2\pi j}}\oint _{C}X(z)z^{n-1}dz\$

and define the DTFT (Discrete-time Fourier transform) and inverse to be totally compatible:

$X(e^{j\omega })=\sum _{n=-\infty }^{\infty }x[n]e^{-j\omega n}\$

$x[n]={\frac {1}{2\pi }}\int _{-\pi }^{+\pi }X(e^{j\omega })e^{j\omega n}d\omega \$

so that in the discrete-time context, one can always substitute $e^{j\omega }\$ for $z\$ in an analogous way that in the continuous-time case we can often substitute $j\omega \$ for $s\$.

9. Greek letters should be used for angles (usually $\theta \$), phase offsets (usually $\phi \$ or $\varphi \$ ), angular frequency (usually $\omega \$), exponential decay coefficients (usually $\alpha \$), and other "exotic" variables. (Sometimes $\epsilon \$ or $\delta \$ for a small error.)

10. Rational transfer functions used in IIR filters or analog filters should have coefficients in the numerator with letters $b_{k}\$ and denominator coefficients $a_{k}\$, often (but not always) with $a_{0}\$ normalized to 1. That is:

$H(z)={\frac {b_{0}+b_{1}z^{-1}+b_{2}z^{-2}+\cdots +b_{N}z^{-N}}{a_{0}+a_{1}z^{-1}+a_{2}z^{-2}+\cdots +a_{N}z^{-N}}}\$

or

$H(s)={\frac {b_{0}+b_{1}s^{-1}+b_{2}s^{-2}+\cdots +b_{N}s^{-N}}{a_{0}+a_{1}s^{-1}+a_{2}s^{-2}+\cdots +a_{N}s^{-N}}}\$

Poles should be $p_{k}\$ and zeros should be $q_{k}\$ so that

$H(z)=A{\frac {(z-q_{1})(z-q_{2})\cdots (z-q_{N})}{(z-p_{1})(z-p_{2})\cdots (z-p_{N})}}\$

or

$H(s)=A{\frac {(s-q_{1})(s-q_{2})\cdots (s-q_{N})}{(s-p_{1})(s-p_{2})\cdots (s-p_{N})}}\$

where $A,p_{k},q_{k}\$ are functions of $a_{k},b_{k}\$ and vise versa.

Of course the $b_{k}\$ coefficients are the same as the impulse response $h[k]\$ for an FIR filter and, in a strictly FIR context, the $b_{k}\$ coefficent symbols should not be used.

11. There should be a section in the Dirac delta article that describes it from our neanderthal engineering perspective (that is as a sorta simple-minded function where the true mathematicians insist it ain't) because it works!

the next time i get back to this i would like to post a (very long) list of articles that would come under this rubric. and i would invite everyone else to do the same. this is not a small clean up i am proposing. but, to do it now is a smaller job than doing it later when the encyclopeia is even more crapped up.

also, of course, please comment on the points i have raised here (interspersed comments are fine). Wikipedia is not "my textbook", but i have thought about this a lot and had tried to keep notational inconsistencies to a minimum in my own writings in the lit as well as in the couple of courses i have taught within the subject (drawing on multiple texts).

thanks for reading. r b-j 05:33, 30 November 2005 (UTC)

Aahh!. I've read all the above, and surprised myself by understanding some of it!. Of course I covered this material many years ago but without use, my memory's faded a bit. Im not a true signal processing engineer like User:Omegatron but I've designed a few analog filters and other analog signal processing circuits in my time. THe only worry I have here on some of your proposals is that they do not seem to be standard in the text books. (like using X(f) instead of f(s). I can see your logic and it is logical, but I fear this may be deemed original research by the WP community and therefore not allowed. However I may be wrong on that.

there's no original research in this. it's just a decision, if we can get folks to buy into it, to set (and enforce, if i may use such a word) a notational convention (or at least eliminate some notational conventions that really are not needed) and use it as consistently as possible to avoid confusion and try to have a little elegance. there is no new or original science or technology. it's just a choice to use some convention over another, even if there are textbooks that use a convention we don't use. r b-j 03:02, 12 December 2005 (UTC)

We have others on the project who know far more than I regarding WP policy and I'm sure they'll pitch in with more comments later just as they did regarding my 'no such thing as second order named filters' claim!

--Light current 07:02, 30 November 2005 (UTC)

i think they are standard but there are multiple standards, not perfectly compatible. A. Bruce Carlson Communications Systems has frequency in Hz and $X(f)\$. many texts of course have the Laplace Transform and $X(s)\$ where $s=j\omega =j2\pi f\$. it is this third convention that has $X(\omega )\$ that i want to eliminate in the Electrical Engineering articles in Wikipedia and replace them with either $X(f)\$ where $\omega =2\pi f\$ or with $X(j\omega )\$ where $X(s)\$ is the Laplace Transform. this way there are only two slightly incompatable definitions of $X(\cdot )\$ and not three. do you see my concern? r b-j 07:18, 30 November 2005 (UTC)

Yes I see! You might be OK with that then--Light current 07:24, 30 November 2005 (UTC)

For what its worth, I agree with 99 percent of what r b-j is proposing, and I also agree that virtually all of his suggestions are more or less quite standard in the Signals and Communications literature. The problem is, as r b-j and others have already discovered, is that there will be quite a bit of push back from others in the WP community. Many people whose primary background is math or physics are not familiar with the conventions that are used in EE. They have conventions and standards of their own, and it is not at all clear that one set of conventions is necessarily better or more correct than any other. The net result is a major clash of cultures that often ends up at best in a stalemate, and at worst, in loud angry exchanges and lots of hurt feelings. I don't know what the answer is, but we need to find a way to achieve consensus and make forward progress. -- Metacomet 08:31, 24 December 2005 (UTC)

i dunno if i have it in me anymore. i've been raped by a couple of admins, the ArbCom doesn't seem to want to do anything about it, and i don't think i'm interested in hanging out at WP anymore. we'll see. sorry for the sour note. have a nice holiday, guys. r b-j 18:09, 24 December 2005 (UTC)

Wait, wait, wait. Don't give up the fight. A couple of days ago, I felt exactly the same way as you do. I have been involved in several really nasty verbal battles. I have been bloodied and bruised, and I am really sick and tired of some of the mindless and inane discussions that go on and on endlessly on some of the Talk pages. But, I have picked myself up and dusted myself off. There is still a lot of room to do good quality work on WP despite the efforts of some to throw up roadblocks and avoid making necessary and useful improvements.

Listen, we need you to stay involved. You hava a lot of good ideas, you understand how to present difficult concepts in a way that is accessible, and you know the difference between good and bad notation. WP is a great concept in theory, but it is clearly not easy to put into practice. Reaching consensus is always a challenge, and it is particularly difficult in this environment. But I think achieving a great outcome will ultimately make the pain worthwhile.

There are some good improvements happening on Discrete-time Fourier transform. We need to keep trying to spread the improvements to all of the FT-related articles. We will succeeed, but you can't give up just yet.

-- Metacomet 18:31, 24 December 2005 (UTC)

Continuous Fourier Transform page

Could users please sign/date all comments -- it makes the page/discussion a lot easier to follow. Also please consider de-indenting (ie removing excess indents from)your posts (below) now we have a heading. THanks--Light current 03:21, 12 December 2005 (UTC)

i'm not gonna bother with de-indenting (i'm afraid of making a mistake, so it hardly seems worth it). i try to pick a (unique) number of indents and stick with it, at least for the time. and if there is any potential for confusion, i might add an indent to someone else's comments so i can keep mine inline and different from the someone else. sorry about interleaving comments and forgetting to sign. but when interspersing comments, i find a sig for every one to be a bit crowded. you should be able to identify by following the same indentation down until that person finally signs. r b-j 05:16, 12 December 2005 (UTC)

Yes thats a good idea - one which i use. But signing after every post does remove all doubt about whos writing (youll get used to it :-)--Light current 06:50, 12 December 2005 (UTC)

---

I agree with a radical standardization of the symbols to be used in similar context. You could create a table similar to the ones on the main page, I don't think anybody will disagree with it.

well, that is the information i am fishing for here. if there is strong (or moderate) disagreement, i am less motivated to work on doing this. if there is some agreement, i hope that other folks than just me can note WP articles that we should target for this.

I'm quite concerned about the Fourier transform definition. In the article Continuous Fourier transform there are lots of information, but it starts with a definition that is different from the one commonly used in signal processing, then introduces in a small section the most general form, finally lists all the properties using the first definition. It would be necessary to clean it up, putting the general definition first, then creating other articles for different values of the parameter, so we could link to a page like Continuous Fourier transform (signal processing). We could do it by ourself, hoping that somebody will improve the article properly, or we may ask the members on Wikipedia:WikiProject Mathematics: they could do it for us...

Is there anybody here ready to improve the Continuous Fourier transform article for this project of Electronics?? Alessio Damato 10:21, 11 December 2005 (UTC)

what would happen if we sorta "attacked" the Continuous Fourier transform article, not to introduce the "Hertz" version of the F.T. (item no. 5 above), but to put all of the ${\frac {1}{2\pi }}\$ scaling in the inverse F.T. making it compatible with the double-sided Laplace Transform except leaving out the $i\$ in the argument. it would be the $X(\omega )\$ convention (which is the one i would like to see left out of the EE articles where there would be either $X(f)\$ or $X(j\omega )\$. this is because it is commonly used in the pure and applied mathematics (and physics) world. also they use $f(t)\$ and $F(\omega )\$ where we would try to reserve $f\$ for (non-angular) frequency. but, even though i understand why some like that ${\frac {1}{\sqrt {2\pi }}}\$ scaling, because there is that in both forward and inverse transform, you don't get all of the beautiful symmetry features that you get with the $X(f)\$ convention in item no. 5 above, so i sorta think "why bother?" i think i'll add a note to Talk:Continuous Fourier transform and see how those guys react. but, from the POV here (mostly EEs, i presume), does fixing that non-standard scaling convention in Continuous Fourier transform and introducing a section with the "Hertz" convention (no. 5 above, with f instead of ω and with j instead of i) as an alternative convention, does that sound like a good idea to you guys? r b-j 03:02, 12 December 2005 (UTC)

The only sure way to tell is to do it, then wait for any criticisms. This is because people can see more easily what you're doing when you've done it. Most folks, Im sure, dont read the talk pages with the proposals and even if they do, they may not understand what it is you're proposing. I dont know the full impact of your proposal, so its best to try it on one article first. Best to take it easy at first I think! I suppose the article you mentioned (CFT)is as good as any. Good luck!--Light current 03:12, 12 December 2005 (UTC)

it's a lot of work (not conceptually hard, but you have to be careful, even anal so you don't have scaling errors in the table of transforms and theorems. i'm gonna check with those guys first. r b-j 03:20, 12 December 2005 (UTC)

i left a note at Talk:Continuous Fourier transform, but, after looking more at the article, i doubt that there will be much support for an adjustment to the principle definition which is unitary. r b-j 05:16, 12 December 2005 (UTC)

First of all, I agree with what you are trying to accomplish. Unfortunately, I think it will quickly become a very emotional and mindless debate over the merits of each different form of the CTFT. I believe that you may want to consider creating separate but linked pages, one for each of the three major conventions, and then a fourth page to act as an overview and a bridge between the more specific pages. I don't mean to rain on your parade, but I don't think you will be able to convince many mathematicians or physicists to go along with your changes unless you find a way to include each of the different forms. See also my comments on Talk:Continuous Fourier transform in the section related to normalization. -- Metacomet 12:47, 12 December 2005 (UTC)

The other advantage of this approach is that you can go ahead and create rough drafts of all of these pages separate from the existing articles by using someone's User page, or perhaps by creating a mini Wikiproject just for this purpose. Then, after you have completed the drafts and worked out all of the bugs, you can begin inviting the community to review the drafts and make comments and/or improvements. Although this may seem like it will take a lot of time, in the end, it may be the fastest way, or perhaps the only way, to get where you want to go. -- Metacomet 12:56, 12 December 2005 (UTC)

IMO, the $\omega$ notation is more compact and easier to use than $f$; the argument that using $f$ involves fewer scaling factors is erroneous, as you now have $2\pi$ in the exponential for both directions! (and these scaling factors are in the superscript, which are harder to read!).

And from an engineering point of view, I use $\omega$ far more often than I use $f$ (admittedly I mostly do comms theory stuff though). If you're doing anything but the most trivial manipulation, it saves the hassle of remembering to bring down the $2\pi$ when integrating, differentiating, etc.

yeah, and you have to remember it when applying duality (but which way does it go?) or convolution (in one domain or the other, but which one?), Parseval's theorem (again, which side is the side i put $2\pi \,$ on? or is it $1/2\pi \,$?) or the fact that $x(0)=\int _{-\infty }^{\infty }X(j\omega )d\omega$ (but which side gets the $2\pi \,$?). if all you're doing is writing down the definition of the F.T. or differentiating or integrating (or delaying or multiplying by $e^{j\omega t}\$, then $\omega \$ is cheaper than $f\$, but $s\$ is cheaper than $\omega \$ so why not just use the Laplace Transform. it's when doing manipulations invloving Parseval or X(0) or x(0) or convolution (in either domain) or rect() vs. sinc() (i dislike how the defined that here, also, we have to call it the "normalized sinc()"), the gaussian pulse, the dirac impulse, the sampling function ("dirac comb") in either domain and across domains (using the duality theorem), that where the $e^{j2\pi ft}\$ does so much better than $e^{j\omega t}\$. all you have to do is remember to put the $2\pi \$ along with $f\$ in the F.T. and carry them along when doing manipulations (like differentiation). but having to remember scale factors when you are actually appling any operations i mention above is virtually eliminated with the $e^{j2\pi ft}\$ way. this is especially useful for continuous-time signal processing (in both domains) which is what you do in comms theory. still think the argument is erroneous?

Hmmm, good points! It seems I didn't think much ahead when I wrote that! I guess that whichever normalisation you use, you'll end up with scaling factors at some point.

As for "why not use $s$", using Laplace Transform hides $j$, and so obscures the effect of quadrature, conjugate, etc. operations. -- Oli Filth 19:41, 13 December 2005 (UTC)

It also makes the transition to manipulating the spectra of discrete signals easier (and then onto the z-transform), where a capital $\Omega$ is more commonly used to indicate angle around the unit-circle, and $f$ is in a sense meaningless. And not to mention the DFT, where you have no choice but to include an overall scaling factor somewhere.

for the DTFT the mapping is from dicrete-time to continuous-frequency (over a finite or periodic interval) so the mapping is not symmetrical like in the continuous FT, so i would suggest simply using the bilateral Z transform with $z=e^{j\omega }\$ where this $\omega \$ is normalized angular frequency (radians per sample). since the symmetry is blown away anyway, there is less to gain with normalized frequency (cycles/sample) because you won't be using duality theorem anyway. more likely you will be using z everywhere during analysis and when you want to finally see a frequency response, you'll use $z=e^{j\omega }\$.

When you say DTFT, do you mean continuous FT of discrete time signals, or the DFT? DFT is symmetric (discrete-time, discrete-frequency), can be made unitary, and has similar duality properties to the continuous FT. -- Oli Filth 19:41, 13 December 2005 (UTC)

The FT article is an article about the pure mathematical aspects of the Fourier Transform. I don't think we should be trying to change it to fit the notation for our particular application; the FT has far more uses than just signal processing engineering (see the comment in Talk:Continuous Fourier transform about unitary transforms, for example. -- Oli Filth 16:52, 13 December 2005 (UTC)

i understand that. what i'm trying to do is spin the different conventions off to their own specialty pages (with their own tables of transforms and theorems which will be quantitatively different because of this scaling issue, and i guarantee that the $e^{j2\pi ft}\$ tables will be much simpler and much easier to remember) but still attach them to the mother Fourier transform page. what i want to avoid is, in an EE comms theory or signal processing article to say "Fourier Transform" or "continuous Fourier Transform" and if the reader decides to look it up or find his way to that page by some means, other than following our specific link to our F.T., i don't want that reader to find absolutely no trace of the F.T. as defined and used in the EE communications and signal processing pages and i refuse to try to fix up these pages without the F.T. defined with $e^{j2\pi ft}\$ because i know there will be a whole shitload of scaling factors that I'll have to remember and deal with. i would rather settle this issue now and save me time in the future than slug this $j\omega \$ stuff out in pages where it is not optimal only to find out next year that someone like me is replacing all of the $\omega \$ with $2\pi f\$. there's a reason for why books like A. Bruce Carlson stuck with the $e^{j2\pi ft}\$ F.T., especially for introductions to the material and that is all we can hope to do here. still think the argument is erroneous? r b-j 18:39, 13 December 2005 (UTC)

Well, I wasn't saying that the whole argument was erroneous, just the bit about being more/less compact notation (which I now admit was probably not erroneous!).

Producing parallel pages could be a good idea in principle, but I imagine it would be a bitch to maintain, and could lead to more confusion if not pages are not very clearly linked. e.g. someone comes to Wiki one day, stumbles upon one version of the FT page, and gets a definition of an FT pair. Then the next day, they stumble upon a different page somehow, and then get a different, seemingly "conflicting" definition. IMO it would be better to leave the one original table, but add a paragraph explaining the rules to convert to a different normalisation (e.g. "substitute $2\pi f$ for $\omega$, scale by...").

However, settling it one way or another is definitely a good idea. -- Oli Filth 19:41, 13 December 2005 (UTC)

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