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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)
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)
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
In my mind group delay is the change in phase as a function of frequency (i.e. phase delay non-linearity). As it stands the current wikipedia entry addresses this only obliquely. Perhaps a useful explanation for signal processing theoreticians who see the world through convoluting FIR filters but not a good explication for others. I suggest that the above article form the basis of the introduction with the beat frequency as an example. In fact I'd extend the example to show the post filter graphic that increases the beat frequency. The existing Laplace description should be retained in a "mathematics" section. —Preceding unsigned comment added by 75.107.113.194 ( talk) 14:44, 8 September 2009 (UTC)
For those of us that can't comprehend what the laplace transform of an integral is, I think this article (or at the very least, the introduction) needs to be simplified. The opening paragraph should give a broad overview of the subject and what it is generally used for. Then, there should probably be a "derivation" section where all of the meaningless formulas can be shown. From reading this article, I have no idea what group delay is, and I'm an engineer that took calculus and differential equations all through college. Snottywong 02:17, 4 May 2007 (UTC)
I have to agree. I have a technical background (more on the computer science side, granted) and had no more idea of what group delay was when I finished the article than when I'd started. I suggest a single non-technical paragraph at the very beginning explaining in layman's terms what group delay is.
Ivan Denisovitch
18:43, 6 June 2007 (UTC)
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)
Is constant group delay the same as True time delay? If so, the later article might be replaced with a redirect to this one. Sohaibafzal ( talk) 07:14, 14 July 2011 (UTC)
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:
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)
I must say that the whole article needs serious improvement. It contains several innacuracies. For example, already in the definition:
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)
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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)
So, about a particular paragraph under the previous headline, "talk:Ungeekification", where that paragraph begins with: "Another kind of linear time invarient (LTI) system works with "baseband" signals and does not involve modulation". That paragraph I believe, is absolutely corrrect. But furthermore, it contrasts related ideas that are at the heart of the confusion people have when trying to understand "Group Delay". (Although 'group delay' and 'phase delay' are intimately related to each other, the article should be entitled only 'Group Delay".) Ohgddfp ( talk) 17:03, 14 March 2020 (UTC)
Here is what I believe needs to be clarified. I think amplitude modulation and demodulation in a radio channel is simple enough to provide a very good example of an LTI system having a particular 'group delay'. In the example, the radio signal (passband) consists of a high frequency sine wave functioning as the 'carrier', and the intelligence in the form of a baseband signal modifying the carrier's amplitude, causing the envelope of the passband signal to be identical in shape with the baseband waveform. Upon demodulation of the radio signal in the receiver, the baseband function is recovered from the envelope of the passband signal. Ohgddfp ( talk) 18:31, 18 March 2020 (UTC)
If the magnitude response and the 'Group Delay' of the above example LTI system are both flat for the aperture (frequency range) responsible for creating a particular envelope, then the time delay of frequency components making up the baseband waveform will not be altered, and therefore the waveshape of that baseband waveform will also not be altered. Besides being flat, the amount of 'group delay' give the time delay of the baseband (and envelope) waveform. Ohgddfp ( talk) 18:31, 18 March 2020 (UTC)
Additional explanation is needed regarding a baseband signal not involved with a modulating (RF) signal: A linear phase LTI filter has a flat group delay, but the inverse is not necessarily true. (A filter with flat group delay is not necessarily a linear phase filter.) The explanation in the aforementioned Ungeekification paragraph is also very revealing on this issue; example graphs matching the words should be included. Ohgddfp ( talk) 18:31, 18 March 2020 (UTC)
For people who work in 'signal processing' a critical function in industry, this article is of high importance. Ohgddfp ( talk) 17:10, 14 March 2020 (UTC)
This section should be removed entirely. There is no group delay in audio. That's because analog continuous time audio signals are directly used in sound reproduction, and are generally baseband signals and not modulated signals. Therefore the LTI system frequency range of interest can have very non-linear phase, giving very bad waveform distortion, and yet still have a perfectly flat group delay in that same frequency range of interest, making the measurement of group delay useless. See the paragraph in "Talk:Ungeekification" that starts with "Another kind of linear time invarient (LTI) system works with "baseband" signals and does not involve modulation." This Wiki section, "Group Delay in Audio", minus the word "Group" could be part of a wiki sound reproduction article, and 'phase' could have a link to a separate wikipedia article that is simply entitled "Signal Phase" or some such thing.
Ohgddfp (
talk)
00:44, 16 March 2020 (UTC)
My previous comments need review. My previous objections to Group Delay in audio stem from authors not mentioning "minimum phase". I am now looking for how to better find reliable sources and talk about them more completely. Now that I have reviewed the helpful links from Binksternet, reading those article pushed me into doing much more research so I can finally make helpful suggestions.
Ohgddfp (
talk)
04:23, 17 March 2020 (UTC)
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:
I just revamped the lead again, adding a mention of the article coverage. Any mention of that was taken out of the Introduction. Ohgddfp ( talk) 18:25, 21 October 2020 (UTC)
changed talk section title to Lead section Ohgddfp ( talk) 17:46, 23 November 2020 (UTC)
Another new lead today. Harmonizes better with the upcoming math. Ohgddfp ( talk) 17:13, 8 December 2020 (UTC)
Referring to 6 above, "time delay of the phase", which I complained about 1.5 years ago, is still in the article. I see it was quoted by at least one forum, so I will correct it now. Ohgddfp ( talk) 21:16, 14 May 2022 (UTC)
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)
I'm looking at the introduction about the 3rd paragraph. About: "Variations in group delay cause signal distortion, just as deviations from linear phase cause distortion." Huh? er What? This gets into it too quick. Many who look up "group delay" have only a weak understanding of these terms. The foundational aspects of group delay is the device's phase response. To understand phase, one must understand "frequency", and to understand "frequency", one must understand at least the fourier series, even though a continuous fourier transform applies more generally. The article should be a development from simple to complex, so that each concept builds on the previous. The fourier series is more understandble at the beginning, and the concepts can be made quite visceral in the reader's mind when frequency spectrums are not continuous. Graphs should be used to illustrate this, eventually leading to the phase response of a system. Both group delay and phase delay can be calculated exactly from the system phase response. Issues dealing with phase are covered first, with some more vivid demonstrations, and then showing how phase delay and group delay come about as tools to more directly analyze signal distortion. Too much math at the beginning is not an efficient route to conceptional understanding. And certainly does not belong in the "introduction", which should only give a definitive use case and how the development of understanding is to proceed. Ohgddfp ( talk) 09:45, 21 October 2020 (UTC)
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) So now I added a Background section.
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)
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)
I am moving the existing math out of the Introduction Section, because it belongs in the heart of the theory. Ohgddfp ( talk) 11:52, 23 October 2020 (UTC)
The introduction was missing a critical condition for group delay of a device passing a "passband" signal equaling the phase delay for "baseband". That critical requirement is that the device phase response in frequency range contained in the signal must be a straight line. I updated both the lead and the introduction accordingly. Ohgddfp ( talk) 17:52, 23 November 2020 (UTC).
I am thinking also that the actual use case for group delay needs to be included in the introduction, emphasizing the benefits of group delay as a measurement tool in the context of a modulated signal, such as relatively easy calculation, especially with an oscilloscope, that reveals some aspects of the baseband signal after demodulation. Already in the article is the special case of a straight-line portion of the device's phase response as it relates to group delay. Also should be mentioned is a specific property and more general property of group delay device property for a modulated signal, in that the group delay function over the frequencies contained in the passband (modulated) signal reveals limits on the maximum possible time delay irregularities of the demodulated baseband signal, but cannot give actual time delay for a given frequency component of the demodulated baseband signal. As I am now preparing the simple math to demonstrate this aspect of group delay, the math itself will inform me of the best wording. So some better wording and graphics that harmonize better with the wording are forthcoming. Ohgddfp ( talk) 15:50, 25 November 2020 (UTC)
Made some clarifying changes in what is now the Introduction Section. Ohgddfp ( talk) 23:33, 14 May 2022 (UTC)
Currently called the "overview", this section outlines the complications of group delay, which is much harder to describe. More focused on the essential idea. No need to talk about cascading as before. Ohgddfp ( talk) 17:15, 8 December 2020 (UTC)
The new introduction, introduced yesterday, is very bad. The first sentence of an article is critical. It should always define the topic. Instead, the new intro's first sentence says that phase and group delay "can be calculated exactly from an LTI device's phase vs frequency property", but gives the reader no clue whatsoever as to what they are, and even introduces additional confusion by introducing the undefined acronym "LTI". I understand the desire to be more rigorous in the lede, but the lede needs to also be clear and easy to understand. -- Srleffler ( talk) 21:48, 15 May 2022 (UTC)
About a recently added sentence from a paper by Leach: "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 [over the bandwidth]." (IMHO, the reader will interpret the quote as if the author included my bracketed expression.) Although the sentence is true, this might lead the reader to believe that exact reproduction can be achieved, even if group delay and phase delay are not flat over the signal's bandwidth, as long as they're equal. But that would be wrong. Ohgddfp ( talk) 06:02, 28 May 2022 (UTC) Ohgddfp ( talk) 05:59, 28 May 2022 (UTC)
And worse, that reader's hypothetical conclusion is wrong for an unexpected reason. It turns out that if phase delay and group delay are not equal to each other, then a requirement for exact reproducton—a flat phase delay—is not achieved. Ohgddfp ( talk) 05:59, 28 May 2022 (UTC)
Under the heading "Group delay in audio", about
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)
First line claims phase delay and group delay (metrics of phase distortion) describes how frequencies are delayed in time for LTI systems, like microphones and loudspeakers, etc. These (passive) devices contain no means to delay anything in time and the whole statement is plain wrong. In reality, for such passive analog devices, these metrics describe phase distortion, not time delays. Further treatment with carrier and wave packets relates to telegraphy, which is (AFAIK) where phase delay and group delay were first treated in relation to electrical signals (by Henry Nyquist). Later, this article mentions negative group delay and that this does not violate causality, which is a big red flag clearly indicating that positive and/or negative group delay (in these passive analog systems, like microphones and loudspeakers) simply cannot be related to time delays (since negative group delay would then imply time advancement). Cfuttrup ( talk) 17:35, 27 April 2024 (UTC)
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![]() | The contents of the True time delay page were merged into Group delay and phase delay. For the contribution history and old versions of the redirected page, please see its history; for the discussion at that location, see its talk page. (21 July 2017) |
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)
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)
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
In my mind group delay is the change in phase as a function of frequency (i.e. phase delay non-linearity). As it stands the current wikipedia entry addresses this only obliquely. Perhaps a useful explanation for signal processing theoreticians who see the world through convoluting FIR filters but not a good explication for others. I suggest that the above article form the basis of the introduction with the beat frequency as an example. In fact I'd extend the example to show the post filter graphic that increases the beat frequency. The existing Laplace description should be retained in a "mathematics" section. —Preceding unsigned comment added by 75.107.113.194 ( talk) 14:44, 8 September 2009 (UTC)
For those of us that can't comprehend what the laplace transform of an integral is, I think this article (or at the very least, the introduction) needs to be simplified. The opening paragraph should give a broad overview of the subject and what it is generally used for. Then, there should probably be a "derivation" section where all of the meaningless formulas can be shown. From reading this article, I have no idea what group delay is, and I'm an engineer that took calculus and differential equations all through college. Snottywong 02:17, 4 May 2007 (UTC)
I have to agree. I have a technical background (more on the computer science side, granted) and had no more idea of what group delay was when I finished the article than when I'd started. I suggest a single non-technical paragraph at the very beginning explaining in layman's terms what group delay is.
Ivan Denisovitch
18:43, 6 June 2007 (UTC)
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)
Is constant group delay the same as True time delay? If so, the later article might be replaced with a redirect to this one. Sohaibafzal ( talk) 07:14, 14 July 2011 (UTC)
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:
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)
I must say that the whole article needs serious improvement. It contains several innacuracies. For example, already in the definition:
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)
![]() | It is requested that a physics diagram or diagrams be
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Jidanni ( talk) 23:28, 11 December 2013 (UTC)
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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)
So, about a particular paragraph under the previous headline, "talk:Ungeekification", where that paragraph begins with: "Another kind of linear time invarient (LTI) system works with "baseband" signals and does not involve modulation". That paragraph I believe, is absolutely corrrect. But furthermore, it contrasts related ideas that are at the heart of the confusion people have when trying to understand "Group Delay". (Although 'group delay' and 'phase delay' are intimately related to each other, the article should be entitled only 'Group Delay".) Ohgddfp ( talk) 17:03, 14 March 2020 (UTC)
Here is what I believe needs to be clarified. I think amplitude modulation and demodulation in a radio channel is simple enough to provide a very good example of an LTI system having a particular 'group delay'. In the example, the radio signal (passband) consists of a high frequency sine wave functioning as the 'carrier', and the intelligence in the form of a baseband signal modifying the carrier's amplitude, causing the envelope of the passband signal to be identical in shape with the baseband waveform. Upon demodulation of the radio signal in the receiver, the baseband function is recovered from the envelope of the passband signal. Ohgddfp ( talk) 18:31, 18 March 2020 (UTC)
If the magnitude response and the 'Group Delay' of the above example LTI system are both flat for the aperture (frequency range) responsible for creating a particular envelope, then the time delay of frequency components making up the baseband waveform will not be altered, and therefore the waveshape of that baseband waveform will also not be altered. Besides being flat, the amount of 'group delay' give the time delay of the baseband (and envelope) waveform. Ohgddfp ( talk) 18:31, 18 March 2020 (UTC)
Additional explanation is needed regarding a baseband signal not involved with a modulating (RF) signal: A linear phase LTI filter has a flat group delay, but the inverse is not necessarily true. (A filter with flat group delay is not necessarily a linear phase filter.) The explanation in the aforementioned Ungeekification paragraph is also very revealing on this issue; example graphs matching the words should be included. Ohgddfp ( talk) 18:31, 18 March 2020 (UTC)
For people who work in 'signal processing' a critical function in industry, this article is of high importance. Ohgddfp ( talk) 17:10, 14 March 2020 (UTC)
This section should be removed entirely. There is no group delay in audio. That's because analog continuous time audio signals are directly used in sound reproduction, and are generally baseband signals and not modulated signals. Therefore the LTI system frequency range of interest can have very non-linear phase, giving very bad waveform distortion, and yet still have a perfectly flat group delay in that same frequency range of interest, making the measurement of group delay useless. See the paragraph in "Talk:Ungeekification" that starts with "Another kind of linear time invarient (LTI) system works with "baseband" signals and does not involve modulation." This Wiki section, "Group Delay in Audio", minus the word "Group" could be part of a wiki sound reproduction article, and 'phase' could have a link to a separate wikipedia article that is simply entitled "Signal Phase" or some such thing.
Ohgddfp (
talk)
00:44, 16 March 2020 (UTC)
My previous comments need review. My previous objections to Group Delay in audio stem from authors not mentioning "minimum phase". I am now looking for how to better find reliable sources and talk about them more completely. Now that I have reviewed the helpful links from Binksternet, reading those article pushed me into doing much more research so I can finally make helpful suggestions.
Ohgddfp (
talk)
04:23, 17 March 2020 (UTC)
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:
I just revamped the lead again, adding a mention of the article coverage. Any mention of that was taken out of the Introduction. Ohgddfp ( talk) 18:25, 21 October 2020 (UTC)
changed talk section title to Lead section Ohgddfp ( talk) 17:46, 23 November 2020 (UTC)
Another new lead today. Harmonizes better with the upcoming math. Ohgddfp ( talk) 17:13, 8 December 2020 (UTC)
Referring to 6 above, "time delay of the phase", which I complained about 1.5 years ago, is still in the article. I see it was quoted by at least one forum, so I will correct it now. Ohgddfp ( talk) 21:16, 14 May 2022 (UTC)
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)
I'm looking at the introduction about the 3rd paragraph. About: "Variations in group delay cause signal distortion, just as deviations from linear phase cause distortion." Huh? er What? This gets into it too quick. Many who look up "group delay" have only a weak understanding of these terms. The foundational aspects of group delay is the device's phase response. To understand phase, one must understand "frequency", and to understand "frequency", one must understand at least the fourier series, even though a continuous fourier transform applies more generally. The article should be a development from simple to complex, so that each concept builds on the previous. The fourier series is more understandble at the beginning, and the concepts can be made quite visceral in the reader's mind when frequency spectrums are not continuous. Graphs should be used to illustrate this, eventually leading to the phase response of a system. Both group delay and phase delay can be calculated exactly from the system phase response. Issues dealing with phase are covered first, with some more vivid demonstrations, and then showing how phase delay and group delay come about as tools to more directly analyze signal distortion. Too much math at the beginning is not an efficient route to conceptional understanding. And certainly does not belong in the "introduction", which should only give a definitive use case and how the development of understanding is to proceed. Ohgddfp ( talk) 09:45, 21 October 2020 (UTC)
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) So now I added a Background section.
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)
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)
I am moving the existing math out of the Introduction Section, because it belongs in the heart of the theory. Ohgddfp ( talk) 11:52, 23 October 2020 (UTC)
The introduction was missing a critical condition for group delay of a device passing a "passband" signal equaling the phase delay for "baseband". That critical requirement is that the device phase response in frequency range contained in the signal must be a straight line. I updated both the lead and the introduction accordingly. Ohgddfp ( talk) 17:52, 23 November 2020 (UTC).
I am thinking also that the actual use case for group delay needs to be included in the introduction, emphasizing the benefits of group delay as a measurement tool in the context of a modulated signal, such as relatively easy calculation, especially with an oscilloscope, that reveals some aspects of the baseband signal after demodulation. Already in the article is the special case of a straight-line portion of the device's phase response as it relates to group delay. Also should be mentioned is a specific property and more general property of group delay device property for a modulated signal, in that the group delay function over the frequencies contained in the passband (modulated) signal reveals limits on the maximum possible time delay irregularities of the demodulated baseband signal, but cannot give actual time delay for a given frequency component of the demodulated baseband signal. As I am now preparing the simple math to demonstrate this aspect of group delay, the math itself will inform me of the best wording. So some better wording and graphics that harmonize better with the wording are forthcoming. Ohgddfp ( talk) 15:50, 25 November 2020 (UTC)
Made some clarifying changes in what is now the Introduction Section. Ohgddfp ( talk) 23:33, 14 May 2022 (UTC)
Currently called the "overview", this section outlines the complications of group delay, which is much harder to describe. More focused on the essential idea. No need to talk about cascading as before. Ohgddfp ( talk) 17:15, 8 December 2020 (UTC)
The new introduction, introduced yesterday, is very bad. The first sentence of an article is critical. It should always define the topic. Instead, the new intro's first sentence says that phase and group delay "can be calculated exactly from an LTI device's phase vs frequency property", but gives the reader no clue whatsoever as to what they are, and even introduces additional confusion by introducing the undefined acronym "LTI". I understand the desire to be more rigorous in the lede, but the lede needs to also be clear and easy to understand. -- Srleffler ( talk) 21:48, 15 May 2022 (UTC)
About a recently added sentence from a paper by Leach: "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 [over the bandwidth]." (IMHO, the reader will interpret the quote as if the author included my bracketed expression.) Although the sentence is true, this might lead the reader to believe that exact reproduction can be achieved, even if group delay and phase delay are not flat over the signal's bandwidth, as long as they're equal. But that would be wrong. Ohgddfp ( talk) 06:02, 28 May 2022 (UTC) Ohgddfp ( talk) 05:59, 28 May 2022 (UTC)
And worse, that reader's hypothetical conclusion is wrong for an unexpected reason. It turns out that if phase delay and group delay are not equal to each other, then a requirement for exact reproducton—a flat phase delay—is not achieved. Ohgddfp ( talk) 05:59, 28 May 2022 (UTC)
Under the heading "Group delay in audio", about
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)
First line claims phase delay and group delay (metrics of phase distortion) describes how frequencies are delayed in time for LTI systems, like microphones and loudspeakers, etc. These (passive) devices contain no means to delay anything in time and the whole statement is plain wrong. In reality, for such passive analog devices, these metrics describe phase distortion, not time delays. Further treatment with carrier and wave packets relates to telegraphy, which is (AFAIK) where phase delay and group delay were first treated in relation to electrical signals (by Henry Nyquist). Later, this article mentions negative group delay and that this does not violate causality, which is a big red flag clearly indicating that positive and/or negative group delay (in these passive analog systems, like microphones and loudspeakers) simply cannot be related to time delays (since negative group delay would then imply time advancement). Cfuttrup ( talk) 17:35, 27 April 2024 (UTC)