Talk:Group delay and phase delay

message: How is group delay defined for a frequency translating device (a mixer)? If the input and output frequencies are different, their phases cannot be directly compared. It would be possible to compare the phase to that of an ideal frequency transliting device. Are there other, better definitions? How can it be measured? (A simple example of a mixer is an AM radio. Signals at several MHz are translated down to audible frequencies).--HelgeStenstrom 13:29, 2 May 2006 (UTC)
thread_title: Untitled

message: i'm a little busy at the moment, but i do want to continue with this rewrite including a couple of drawings that i haven't done yet.  as i said in the move comments, i want to start with first principles where both group delay and phase delay are defined and then have the article go over the specific places where group or phase delay (mostly the former) are used (optics, transmission lines, audio, etc.). also, thanks to User:81.240.215.127 for correcting my convolution integral mistake.  r b-j 17:41, 6 March 2007 (UTC)
thread_title:  article move and revamping. 

message: The article below provides a **much** more intuitive explanation of what group delay is:
http://sep.stanford.edu/sep/prof/pvi/spec/paper_html/node19.html
BB
:I do believe the concepts in the Standford article are mostly at the heart of what this Wiki should get across. But not everyone can follow the equations very well. A much simpler explanation of the same concepts is possible, and at each stage should be accompanied by graphs, along with the equations that go with those graphs. Ohgddfp (talk) 02:11, 16 March 2020 (UTC)
replies: text: About: "... group delay is the change in phase as a function of frequency ...":  How about "... group delay is the rate of phase change as the functon of frequency? Ohgddfp (talk) 17:43, 18 March 2020 (UTC)
thread_title:  Big Improvement Possible ... 

message: I think in this section one of the author names is Blauert (with a 't' at the end). I tried to change it but it doesn't seem to be effective. Maybe it has something to do with the referencing thing. Sorry I don't have time to look into this now, so if someone knows what's wrong...  — Preceding unsigned comment added by 82.66.50.169 (talk) 09:23, 25 May 2011 (UTC)
thread_title:  Authors in section "Group delay in the audio field" 

message: The threshold in the presented table [500 Hz	3.2 ms, 1 kHz	2 ms, 2 kHz	1 ms, 4 kHz	1.5 ms, 8 kHz	2 ms] needs additional information from the cited paper:
:1) Values are for diotic presentation (monotic presentation show similar thresholds; also, the monotic ones are presented only for 1,2 and 4 kHz)
:2) Values are for bandlimited sound impulses under unechoic conditions (25 micro seconds-wide rectangular impulses) - the thresholds for 'speech, noise, music, harmonic series' were found to be higher but not presented in the study
:3) Values are not presented for trained subjects - from their experiment, the threshold halved at 4 kHz for one trained subject: from 0.86 to 0.4 ms. So, for 'worst case' the thresholds are actually lower.
:4) Tested method was paired forced-choice [compared to the final test they did - triadic method, forced choice]
The table might need the word threshold for 'group delay', since it is not clear if the values are for group delay or phase delay.
I would mention these facts so that people would not take those values as they are. At least mention that more popular types of signals (music for instance) have higher thresholds. Also that these are for anechoic conditions.
For the worst-case scenarios (trained subjects), the thresholds are actually lower and are not reported for all frequencies.  — Preceding unsigned comment added by 5.13.214.42 (talk) 16:31, 23 December 2012 (UTC)
thread_title:  Thresholds for group delay need more information 

message: I must say that the whole article needs serious improvement. It contains several innacuracies. For example, already in the definition:
* Group delay is not a definition for "signal processing". It is an efect tha happens to any signal that travels through any linear system. Signal processing makes use of it, as for example also does microwave engineering, analog filter designers, or communications engineering.
* In the article it is stated that group delay affects to "signal amplitude" and phase delay affects to "signal phase". This is deeply untrue.
* It links group delay with audibility. That is nonsense, because the audibility of any signal is independent of the precise instant it arrives. I strongly guess that he refers to "group delay dispersion".
* etc
I strongly suggest a complete rewrite of the article.  — Preceding unsigned comment added by 138.4.36.49 (talk) 10:34, 17 January 2013 (UTC)
replies: text: Well, feel free to be wp:bold.  The worst that can happen is that your edits get reverted.  As best as I can tell, the math in the Introduction section is completely correct.  The group delay applies to the "group" or envelope of a modulated sinusoid.  The phase delay applies to the phase of the sinusoid.  The optics and audio sections I haven't paid much attention to. 71.169.181.144 (talk) 18:40, 17 January 2013 (UTC)
thread_title:  Incorrect statements 

message: Jidanni (talk) 23:28, 11 December 2013 (UTC)
thread_title: Add some diagrams

message: Hello fellow Wikipedians,
I have just modified one external link on Group delay and phase delay. Please take a moment to review my edit. If you have any questions, or need the bot to ignore the links, or the page altogether, please visit this simple FaQ for additional information. I made the following changes:
*Added archive https://web.archive.org/web/20150930080912/https://community.klipsch.com/forums/storage/3/1027021/7805blauert.pdf to https://community.klipsch.com/forums/storage/3/1027021/7805blauert.pdf
When you have finished reviewing my changes, you may follow the instructions on the template below to fix any issues with the URLs.
Cheers.—InternetArchiveBot (Report bug) 16:54, 25 March 2017 (UTC)
thread_title:  External links modified 

message: This article is a perfect example of the need for an "Einsteinian" explanation, where Einstein said, "Everything should be made as simple as possible, but no simpler." Ohgddfp (talk) 17:03, 14 March 2020 (UTC)
thread_title:  More Ungeekification 

message: I am changing the lede, part of a series of improvements to this article. The subject matter is difficult to explain and understand, even for engineers.  The characterization of some changes and other changes to come are:
:1) Accessible.  Must be as simple as possible while still being entirely correct.  The emphasis must be on conceptualization.  To that end, no unneeded jargon.
:2) The topic is abut the mathematically quantifiable properties of signal processing devices such as amplifiers or filters. Anything other than how they are quantified is not real, and is off topic.
:3) The current lede (before my changes) mentioned "envelope". This is actually confusing for two reasons: One, in amplitude modulation, although the period of the intelligence (baseband modulating signal) is identical to the period and shape of the envelope, the frequency that is likely to be inferred regarding the passband signal does not exist in the passband signal at all, but exists only in the baseband signal. This is a point of very common confusion.  And two, with other kinds of modulation more common these days, FM broadcast, complex modulating schemes like QAM, FSK and other digital signaling, SSB, often does not show a discernable envelope when looking at the passband (RF) signal.  So in terms of gaining a conceptual understanding, "envelope" is more likely to mislead rather than inform at an early point in the article (like the lede).
:4) Group delay, as mentioned by others on this talk page is quite complicated in concept.  For example, it cannot give any difinitive or quantifiable information outside the context of modulation and demodulation.  And group delay cannot even give the time delay of the DUT frequency components.  Instead, in that context (mod and demod), group delay only gives the phase delay that the passband DUT contributes to the system as a whole, where both system input and system output are both baseband.  Correcting this point of common misconception is so important that is should be in the lede.
:5) "function of frequency for each component" ? ? ?  The frequency is the component.  Yes, group delay is indeed a function of frequency.
:6) "time delay of the phase" ? ? ? ?  Well, time delay predicted (given) by the phase delay property.  Yes, both group delay and phase delay can be calculated correctly from the phase response of the unit under test.
:7) Lnear phase?  The "offical" term means that the phase response of the DUT goes through the origin.  But for people just learning or brushing up on this stuff, "linear" also can mean "straight line" that does not go through the origin.  But that would not really be linear phase in the technical sense, and such a phase response would indeed cause waveform distortion due to phase irregularities of the DUT.  All this, plus the needed graphs and lots of explanation cannot fit into a reasonable lede.  At this point, early in the article, the phrase only confuses without helping much.  — Preceding unsigned comment added by Ohgddfp (talk • contribs) 16:54, 20 October 2020 (UTC)
thread_title:  The Lead Section 

message: Hi all.  I noticed that the so-called lede that I put up only hours ago looks more like an introduction, so I'm adding it to the beginning of the existing introduction.  I am also re-instating some of the original lede, but heavily re-written. Ohgddfp (talk) 22:37, 20 October 2020 (UTC)
thread_title:  Moving the lede to be part of the introduction.  Also writing a new lede. 

message: === Time to add background - Intro Changed a bit - What the background section entails ===
In the introduction, about: "Variations in group delay cause signal distortion, just as deviations from linear phase cause distortion."  Well, yes it does, but not the other way around.  Severe distortion caused by phase irregularities can easily occur in the frequency band of interest where the group delay is perfectly flat.  Better not to bring this up until the reader has the "why and where for" of this.  I already altered some of the material in the introduction. Now is the time to add new sections to address development of group delay and phase delay theory, starting with a gentle but quantitatively correct treatment on the fourier series. Ohgddfp (talk) 10:08, 21 October 2020 (UTC)
thread_title:  Background Section 

message: In the introduction, about: "Variations in group delay cause signal distortion, just as deviations from linear phase cause distortion."  Well, yes it does, but not the other way around.  Severe distortion caused by phase irregularities can easily occur in the frequency band of interest where the group delay is perfectly flat.  Better not to bring this up until the reader has the "why and where for" of this.  I already altered some of the material in the introduction. Now is the time to add new sections to address development of group delay and phase delay theory, starting with a gentle but quantitatively correct treatment on the fourier series. Ohgddfp (talk) 10:08, 21 October 2020 (UTC)
thread_title:  Time to add background - Intro Changed a bit - What the background section entails 

message: I still need to add a figure for this.  I know about a nice animation in Wiki Commons for this, but I want to emphasize the details in the degrees, and also stick only with the more familure sine. It's easier to examine if nothing is moving. The next subsection is "Phase".  I also need to insert something about fourier, which will be in the form of a lab experiment simulation, do-able in real life for 100 years now. Anyone can try this at home to get a visceral understanding of fourier series.  Also some cosines multiplied by cosines, cosines multiplied by sines, etc.  Some math will accompany this to show how it plays out quantitatively. Ohgddfp (talk) 10:58, 21 October 2020 (UTC)
thread_title:  Added Basic Sinusoid - What's Next 

message: I made changes to the introduction.  The heart of the article (plus the background theory section) will include simpler mathematics that still correctly quantifies in a mathematical and practical sense, all of the issues related to the topic.  I do have plans to, later in the article, to use the higher level math that is already there.  Such math, as it is certainly higher level to most readers, certainly doesn't belong in the introduction. Although the info about "approximations" seem right, I am uneasy about any discussion of approximations until the math with no approximations is covered first.  To aid conceptual understanding, it' much easier (and the math is much easier) to deal with a "group of frequencies" in a literal sense, where the frequency spectrum is only the dirac impulses that result from the periodicity of test signals.  For a useful actual signal, where the intelligence is always new information rather than an endless repeat of the same old information, an aperiodic signal requires the continuous fourier transform, which will also be covered by building on the simpler math that comes before it. Ohgddfp (talk) 18:44, 21 October 2020 (UTC)
replies: text: It looks like it was reverted, which may be for the best right now. The lede is way too long anyway. I agree with some of the critisism. LTI should read "Linear Time Invariant (LTI)", which should be a link to the definition because a system needs to be substantially linear in order for the topic of this article to have a consistent meaning.  Also, since this article is based on the concepts of simply "Phase", this should be a link as well. So I will put in a new lede. If the reader does not understand the concept of a function, there is no hope for the article to be useful to such a (normal person) reader.  So group delay and phase delay are complicated concepts, even for engineers. Understanding of the meaning of the links is a pre-requisit for grasping the concepts of this article. Otherwise it will be gobbledygook for all readers.  For example, the link "topics in [[signal processing" gives the reader advance notice that that link must be understood first.  If a reader starts to become interested signals and signal processing, the reader will probably start with the links. Ohgddfp (talk) 21:16, 23 May 2022 (UTC)

text: I see in the above comment I was confusing the lede with the introduction.  As far as the lede is concerned, it covers the general idea and has links to the other wiki pages that are absolutely required for the reader to move onto the deeper and more specific understanding in the Introduction.  In other words, the lede links are a pre-requisite for further understanding of the topic. The lede was very long with many redundancies and some inaccuracies.  I was able to shorten the lede and still give the prerequisites as links.  If the prerequisites are not somewhat understood by the reader than IMHO, the reader has no hope for any deeper understanding. Ohgddfp (talk) 01:03, 24 May 2022 (UTC)

text: I would like to discuss the underlining for the italizided sentence.  This sentence is the single most revealing difference between Group Delay and Phase Delay, and I think the formatting should reflect this.  Thoughts? Ohgddfp (talk) 20:31, 26 May 2022 (UTC)
replies: text: We don't generally use underlining for emphasis on Wikipedia. Stick with italics for emphasis. This is probably covered somewhere in the Manual of Style.--Srleffler (talk) 21:34, 28 May 2022 (UTC)

text: About "A varying phase response as a function of frequency, which can be described in terms of group delay and phase delay":  Yes, phase response indeed can be described in terms of phase delay.  But in general, phase response cannot be described in terms of group delay. That's because group delay, being a derivative of the phase response, looses the constant term of the phase.  If we try to integrate group delay to get back to phase response, without any priori knowledge of the phase response, we can't because the constant term in the integrand is unknown.  How to modify this paragraph to reflect this reality ?  (By the way, the other way around, group delay being described in terms of phase response does work.) Ohgddfp (talk) 03:01, 29 May 2022 (UTC)
replies: text: I think it is correct as written. The group delay and phase delay together describe the phase response.--Srleffler (talk) 16:44, 30 May 2022 (UTC)
replies: text: Well, my position is that they do not "...together describe the phase response."  Phase delay alone can correctly describe the phase response.  Here's proof.  Phase delay--a function of frequency measured in radians per second--is denoted as "tau as a function of omega". So phase delay is defined as:  \tau_\phi(\omega) = - \frac{\phi(\omega)}{\omega} \ , where phase response is denoted as "phi as a function of omega".  This equation can be algebraically manipulated into  \phi(\omega) \ = -    \tau_\phi(\omega) \omega  .  In words, the phase response, "phi_as_a_function_of_omega", equals minus "tau_as_a_function_of_omega" multiplied by omega.  This demonstrates phase delay alone as being able to completely and correctly, all by itself, describe the phase response. Not only is group delay not needed to describe phase response, group delay cannot even help describe phase response, due to group delay missing the (possibly non-zero) constant term of the phase response. Ohgddfp (talk) 13:13, 31 May 2022 (UTC)
thread_title:  Introduction Section 

message: Under the heading "Group delay in audio", about
:"The waveform of an audio signal can be reproduced exactly by a system that has a flat frequency response over the bandwidth of the signal and a phase delay that is equal to the group delay. Leach[15] introduced the concept of differential time-delay distortion, defined as the difference between the phase delay and the group delay, which is given by:
::  \Delta\tau = \tau_\phi - \tau_g .
:An ideal system should exhibit zero or negligible differential time-delay distortion.[15]":
I cannot find a single actual specific real life example of a use case for this differential time-delay distortion measurement, other than in the founding document by Dr. Leach.  So this cannot be an example of "Group delay in audio" where no example of its gainful use exists.  I therefore recommend its removal. Ohgddfp (talk) 23:13, 5 June 2022 (UTC)
replies: text: Is the concept useful for theoretical analysis? Not everything has to be practically applicable "in real life" to be worthwhile.--Srleffler (talk) 03:20, 6 June 2022 (UTC)
replies: text: If the concept is useful for theoretical analysis, let's use it to theoretically analyze something that will support "Group delay in audio", where using another simpler concept, already covered in this wiki article, is not as enlightening. (Also, the analysis should include a plausable hypothetical example.) Ohgddfp (talk) 03:59, 6 June 2022 (UTC)
thread_title:  Differential time-delay distortion