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I'm not entirely certain what wiki policy is on this, but I've got to assume that any encyclopaedia article should be at least partially understandable by laymen, especially if it's about a topic that directly effects the general public. The reason I ask is that I've seen so many video game reviews (and now DVD review of South Park) which complain about aliasing, and I wish I knew what they were talking about. You'd think that video game reviewers would better explain how aliasing causes problems, but right now, I honestly don't know what the aliasing problems are in my games. - Darkhawk
Ok. You guys don't actually understand what the article says. The word aliasing describes two different but related phenomena. The first is when two different signals are mapped to the same sampled signals (signal->sample is not injective). That is what the smileys were about. The second is about when the signal->sample->reconstruction gives surprising results. That is what the moire patterns in the brick wall are.
Loisel
22:17, 1 March 2007 (UTC)
I wrote probably over half of this article and for a long time I was defending it against non- experts who only have a rudimentary grasp of what aliasing is, but I'm not so sure I care anymore.
Defocusing your lens is again not the same as what the smiley faces represented. Defocusing your lens does not make the pixels big. In fact, you can recover a focused image from a defocused image if you know what you're doing (it's called
deconvolution.) However, you can't recover the smileys from the pixelized image I gave. They're aliased.
Loisel
22:17, 1 March 2007 (UTC)
In statistics, signal processing (including digital photography), computer graphics, and related disciplines, "signals" that are essentially continuous in space or time must be sampled, and the set of samples is never unique to the original signal. The other signals that could (or did) produce the same samples are called aliases of the original signal. If a continuous signal is reconstructed from the samples, the result may be one of the aliases, which represents a form of distortion. The term aliasing can refer to both the ambiguity created by sampling and to the subsequent distortion.
For example, when we view a digital photograph, the reconstruction (interpolation) is performed by our eyes and our brain. If the original image was a lawn, we no longer see the individual blades of grass. Therefore we are seeing an alias. A more interesting example (below) is the Moiré pattern one can observe in a poorly pixelized image of a brick wall. Techniques that avoid such poor pixelizations are called anti-aliasing.
Digital imaging is an example of spatial aliasing. Temporal aliasing is a major concern in the analog-to-digital conversion of video and audio signals: improper sampling of the analog signal will cause high- frequency components to be aliased with genuine low-frequency ones, and to be incorrectly reconstructed as such during the subsequent digital-to-analog conversion. To prevent this problem, the sampling frequency must be sufficiently large and the signals must be appropriately filtered before sampling.
-- Bob K 14:14, 3 March 2007 (UTC)
-- Bob K 15:19, 4 March 2007 (UTC) (revision)
I've taken a stab at a more accessible first sentence, putting the intro more in line with WP:LEDE. ENeville ( talk) 18:28, 28 May 2009 (UTC)
I have an aliasing error versus sampling rate plot taken from Jud Strocks, Telemetry Computer Systems book, I copied. That plot illustrates the RMS error vs sampling rate when using a Butterworh filter with different pole numbers. I would be glad to share it if you want.--Scipio-62 18:49, 23 March 2010 (UTC)
I added this section as a further example that the conventional wisdom of sinc filters isn't always true. Sinc filtering the measured image g, regardless which sinc filter is used, does not lead to any accurate measurement of the radius of the star.
Rnt20 06:37, 11 April 2006 (UTC)
The diameter of Betelgeuse was originally measured in this way. You are incorrect when you say this method was never used to measure the diameter of a star.
Do not remove this example.
Loisel 14:45, 11 April 2006 (UTC)
In my experience, this also happens when watching a spoked wheel. Can someone confirm? (or is this maybe evidence that I'm living in the Matrix... hm, my head hurts now ;-) -- Tarquin 15:26 Dec 20, 2002 (UTC)
This could be the case if your eye samples the scene - perhaps periferal vision does this. I sometimes get a related effect if I see a TV screen or other flickering source out of the corner of my eye - the flicker frequency appears to be much less than 50Hz. -- Easter 15:32 Dec 20, 2002 (UTC)
For really freaky effects, try watching a TV screen or CRT monitor while using an electric toothbrush. The image wobbles up and down, it was quite alarming the first time I saw it. -- Tarquin
This is what my colleagues in broadcast engineering call the ginger biscuit effect. Any vibration to the head will do. -- Easter 15:47 Dec 20, 2002 (UTC)
I think we need an article on this! -- Tarquin
This effect is caused by a failure of persistence of vision, although it could also be regarded as a kind of aliasing (with the vibration of your head providing the sampling frequency). I don't believe that the eye normally does any sampling in the time domain, at least not in a periodic way. Devices like CRT monitors rely on your persistence of vision, which is the slow response of your retina to changing or flickering images. This only works if your eye muscles can produce a stationary image on the retina. When you move your head faster than your eye muscles can track, as happens when you eat crunchy food, the TV image is spread out over your retina and appears fragmented, because parts of your retina see one field of the image and other parts see the next field, or the few milliseconds of darkness between fields. I'm guessing that this effect is more noticeable at the edge of the field of view, because the mechanism that stabilises the eyeball mainly uses data from the centre of the retina. -- Heron 11:30, 31 Mar 2004 (UTC)
I agree -- we need an article on this! What to call it? Recently I've heard it called the "Dorito effect", but Google Fight tells me that "Frito effect" is far more popular. Or is there some other name that would be better for a "serious" (?) encyclopedia article? -- DavidCary 07:13, 14 October 2005 (UTC)
The Frito Effect the Frito Effect Aliasing - A new perspective
Maybe this isn't exactly the same effect, but the most compelling example of this kind of phenomenon I have ever seen occurs when in a dark room, viewing one of those old digital alarm clocks with the red numbering (search for "digital alarm clock" in google images - first few examples are what I'm talking about) just off center, and moving your head around quickly... not violently fast, but fairly fast. The image of the numbers will appear to not be able to keep up with the physical clock, and drift off it to the left and right, up and down, pretty fair distances if you do it just right. —Preceding unsigned comment added by 66.31.7.121 ( talk) 02:51, 3 February 2008 (UTC)
This article has a See Also to
Wagon-wheel_effect, which links to
Temporal aliasing, which is re-directed back to here. Here we point out that sin(-wt+θ) = sin(wt-θ+π) = cos(wt-θ+π/2). So I'm curious why our brain perceives the wheel rotating backward (analogous to sin(-wt+θ)) instead of forward. Most optical illusions, such as the
Ames window and
Ames room occur when our brain tries too hard to interpret what it sees in terms of what it already knows, such as rectangular windows and wagon wheels rotating in the forward direction.
-- Bob K ( talk) 15:43, 7 March 2012 (UTC)
OK, so far, so mathematical, but the article now uses no fewer than four different kinds of L: can the sampling mappings please be called something different, to avoid confusion?
That's ok, but I'm not sure that attempt is optimal. Perhaps and or would be better. You have to be careful to change all the references to and if you do that, they are used consistently throughout the article. I'm going to wait and watch, but if you want me to do it, and have a notation suggestion, just let me know here. Loisel 00:40 Jan 28, 2003 (UTC)
I have a question regarding this paragraph:
The term "aliasing" derives from the usage in radio engineering, where a radio signal could be picked up at two different positions on the radio dial in a superheterodyne radio: one where the local oscillator was above the radio frequency, and one where it was below. This is analagous to the frequency-space "wrapround" that is one way of understanding aliasing. However, there is a deeper way of understanding aliasing, based on continuity arguments, which is outlined below as an introduction.
This is very interesting to me. I am not completely certain that this crosstalk between radio stations is covered by the "outlined below as an introduction" portion. Unfortunately, I am not a physicist (or an engineer) so I don't know what's actually going on.
I think it would be great if someone who understands the long-winded L^2 stuff I wrote could tell me how that relates to the radio waves. I mean, the wrapping around of frequencies I describe depends completely on using a simple sampling scheme (like S_0) and so it's mostly for digital signal processing. In the analog world, I'm not exactly sure what's going on.
If anyone can give us more details about the underlying physics of the radio wave crosstalk phenomenon described above, perhaps there's a section in the aliasing article that needs to treat the analog aliasing process separately, which might be different from the dsp aliasing stuff Loisel 01:38 Jan 28, 2003 (UTC)
The subsection numbers under "technical discussion" serve a purpose: the introduction to "technical discussion" refers to these sections by number. If you want to remove the subsection numbers, you'll have to change the introduction as well. For reference purposes, Encyclopedia Britannica uses numbering for some of its articles (my 1973 copy of World Wars has a complicated numbering system.) Loisel 18:49 Jan 28, 2003 (UTC)
I'm referring to this: In engineering, the method introduced in the third section is called sampling, while a method such as that introduced in the fifth section is called filtering. This discussion may be viewed as a theoretical introduction to the ideas of anti-aliasing. Loisel 18:51 Jan 28, 2003 (UTC)
An article titled "Bishop", after hundreds of words on concept of "bishop" used in religion, had a one-line comment that a piece in chess is called a "bishop", with an appropriate link. I moved that to the beginning of the article where it would actually be seen be anyone interested. I've done the same thing here with the meaning of "aliasing" in computer science. Michael Hardy 19:18 Jan 28, 2003 (UTC)
Hfastedge, don't pollute carefully written articles with your requests. That's what the talk page is for. Loisel 07:29 30 Jun 2003 (UTC)
WHAT THE HELL HAPPENED? Loisel 17:55, 29 Jul 2003 (UTC)
What's this 4LIQ9nXtiYFPCSfitVwDw7EYwQlL4GeeQ7qSO business? Evercat 17:59, 29 Jul 2003 (UTC)
Please don't use <math> in headers. Use a proper substitution. —Eloquence 18:01, 29 Jul 2003 (UTC)
Can someone fix the mathematic notations in the article?
What we need is ONE simple picture showing a sinusoid being sampled at too high rate and matching a lower-frequency sinusoid. Then we can probably delete some 10,000 words... Jorge Stolfi 20:46, 23 Mar 2004 (UTC)
The picture added is good for understanding the time domain aspect of aliasing. However, the reconstruction distortions are based on frequency domain filtering. I'm going to try to find a good picture for that. Mojodaddy 05:22, 20 December 2006 (UTC)
I found a good one, it's found here as the lower picture: http://efunda.com/designstandards/sensors/methods/DSP_Aliasing.cfm?search_string=aliasing It's far more insightful than the current discrete frequency picture. If someone could replicate something similar to that, that'd be awesome. 130.85.235.240 22:29, 21 December 2006 (UTC)
The "Technical description" section was way too long and too heavy on math, it confused more than clarified the concept. Thus I have done some rather radical trimming and replanting.
Specifically, I moved most details of the "reconstruction" sections to a new page signal reconstruction, keeping only the definition of the "standard" reconstruction R. I also deleted the following paragraph since it was not germane to "aliasing"; it should go to some other page (Fourier analysis?):
The following paragraph was deleted too; perhaps it should go to signal processing:
The following paragraphs did not seem to make sense: given that "signal" was defined as a *function*, it would seem that is always well-defined in that case. Perhaps this text was assuming that a signal could be a *distribution* (such as, e.g., Dirac's)?
The following section has the same problem, and it also assumes non-trivial concepts of wavelets etc., so it should probably go elsewhere, too:
Finally the discussion of the operator does not seem to be very useful. The operator does not eliminate aliasing, it only reduces it. On the other hand, when addressing this topic one MUST discuss the sinc filter (which does eliminate aliasing) and the Gaussian filter (which does a pretty good job, and is free from ringing). In any case, this material should be in anti-aliasing, not here.
Jorge Stolfi 01:55, 25 Mar 2004 (UTC)
The sound example needs more explanation: what is the sampling rate, what exactly is meant by "bandlimited", and what should the listener pay attention to. Jorge Stolfi 18:43, 24 Mar 2004 (UTC)
Having specifically said that the Nyquist condition is simplistic, I don't think the following theory adequately explains why this is the case. I mean, it may explain it, but it doesn't specifically summarize why it is that the Nyquist criterion is therefore simplistic. I don't think readers should have to dig so much, only to find vague statements under caveats -- Tlotoxl 10:15, 31 Mar 2004 (UTC)
Shouldn't there be a mention about aliasing in TV broadcast? The reason why moderators don't have certain patterns of dress and so on. Just a thought. 84.42.132.48 11:31, 1 September 2005 (UTC)
Right at the start of the article, where it says:
shouldn't that be analog-to-digital not digital-to-analog or am I just confused?
This paragraph seems to by trying to say that aliasing occurs when you sample analog to digital. It says improper sampling of the analog signal will cause... That seems to imply that analog is the source in this paragraph.
It seems confusing as written, someone who knows better please help me understand this. HighInBC 18:12, 27 February 2006 (UTC)
Thanks. HighInBC 23:58, 27 February 2006 (UTC)
Can someone explain the new animated example. It seems way too busy and confusing. Do we really need animation for this? Can it be explained with some commentary at least? I'm going to take it out for now. Please comment if you like it, or put it back with commentary, or make a more accessible example. Dicklyon 02:44, 4 July 2006 (UTC)
Hi! I believe that is really useful and powerful, though I think there is a small mistake. If we see one single gif frame, we can clearly understand that the main common frequency of all the plotted components is 0.5Hz =30rpm (assuming that the sampling rate is correct). But the title clearly states that the cam-follower is running at 200rpm (which doesn't have much to do with 30rpm). Therefore, either I'm missing something or there is a mistake somewhere. —Preceding unsigned comment added by 93.56.195.203 ( talk) 17:23, 30 April 2011 (UTC)
Apparently I've made no progress getting Rbj to understand the notion of mathematical implication, and the difference between a provably true theorem and its not-always-true converse. He has come over here to spread his joy, having "crapped up" (his words) the Nyquist–Shannon sampling theorem article in the last day or two. He has a narrow view of aliasing based on baseband reconstruction, which he is also mixing up with the notion of an alias itself. My changes are individually documented to indicate the errors in what he has done. Dicklyon 15:43, 17 August 2006 (UTC)
I don't thing there's a lot of point having a separate article for this that contains three sentences, all of which are already implied by the content of this article. Any reason not to just redirect it to here and remove the link from this article? JulesH 09:56, 21 November 2006 (UTC)
Done. I hope you're OK with it, CB. Dicklyon 05:55, 23 January 2007 (UTC)
The POV "ancillary comment" about that linked PDF sounds like something I may have written in my early wikipedia days; if so, it sure lasted a long time, but you're right it sure doesn't belong. Anyway, specific complaints about the Lavry PDF include:
So, now that the disclaimer is gone, I think I'll remove the ext link, too. Dicklyon 21:38, 22 January 2007 (UTC)
Bob K had updated first paragraph to say:
Several problems here. It is ALWAYS true that , the way he defined it, but the text can appear to be saying that is the smallest; it's unclear if this was intended, or is just an incorrect reading of it, but it's confusing.
Dicklyon
19:15, 28 February 2007 (UTC)
And if this was patched up, the "(and only if)" bit is still incorrect, unless you go to the trouble of separately excluding f at the Nyquist frequency.
But it seems to me that this change is not well motivated. The way it's stated now makes the "folding" or "mirroring" property of aliasing more explicit. The folded term is the usual main term that you need to care about, and the absolute value obscures more than clarifies, I think.
Dicklyon
19:15, 28 February 2007 (UTC)
In my opinion, the section on subsampling a sinusoid is really unclear and poorly done. — Preceding unsigned comment added by 137.53.91.144 ( talk) 21:51, 23 February 2012 (UTC)
In section 5.1, we have:
In section 5.6, we conclude with:
In case it isn't obvious, I think what we are saying is that an anti-aliasing filter (and a rectangular one at that) is a good thing to do before sampling.
But how do we confine a sinc function to the interval [0,1]? Is that why we need the "some sort of" caveat? And how do we design a "sort of sinc" filter?
Frankly, these sections don't do much for me. Why "teach" functional analysis here? The relevant points seem to be these:
Am I missing something? Are these unsurprising (and in some cases vague) points enough to justify section 5?
-- Bob K 14:18, 10 March 2007 (UTC)
I think this section may be largely incorrect, or at least somewhat wide of the mark. In my recollection, and what few revelant refs I've been able to find, an alias in radio is just am image frequency. Most of the discussion about spectrum reversal seems not quite relevant. The point of aliasing is not so much that you have a choice of high-side or low-side local oscillator, but that after you've chosen you still have to fight the image or alias from the other side. Is there a book that either makes this clear or supports the current text? Dicklyon 16:58, 18 March 2007 (UTC)
I added the "expert needed" tag. I used to keep an eye on this page but I have stopped and there's some nonsense in there now, but I don't have time to take care of it. I hope the current editors do find an expert. Loisel 01:46, 21 June 2007 (UTC)
Hello again. Some random comments:
Did you intend to keep both of these redundant statements?:
The sun example that you removed predates my involvement. I just fixed it up a bit. I am sorry to see it go away, but no biggie. However, removing it also removes the reason for introducing the symbol so early in the article. Consider postponing its introduction until it is needed.
And it also removes the concept of negative frequency (like a wagon wheel going backward). So now the statement: "And the concept of negative frequency is not necessary, because there is always an identical sinusoid with a positive frequency..." just appears out of nowhere. But I would not advise removing the concept of negative frequency. I think it is useful and interesting to make the point that some phenomena, such as sun motion and wagon wheels and complex sinusoids, are directional and require signed frequency, but real-valued sinusoids do not.
-- Bob K 13:02, 21 June 2007 (UTC)
Ok, well known, but incorrect. No way can I go with folding over negative frequency. Putting people on completely the wrong track is not better than telling the truth, even if the truth takes a little more work to get clear. I'll read up on how Wikipedia & editing works, but I added a comment to this effect today & had it removed by Oli Filth. Sorry mate, wrong. Improve it by all means, but there is no mechanism for "folding" & we should no proliferate the misunderstanding. As I said, I'll try to make time to learn enough to do the job properly, but maybe one of you guys who do this all the time could just deal to the "folding" thing & set it straight to save me the trouble. —Preceding unsigned comment added by Nanren888 ( talk • contribs) 07:48, 31 August 2007 (UTC)
I am bound to repeat some points already made above, but for what it's worth:
Consider a Fourier transform shaped like an isoceles triangle with its peak at 0 Hz and a base width (two-sided) of 12 Hz (i.e., ±6 Hz). Now sample the waveform at Hz. In the region between 4 Hz and 5 Hz (), it looks like the [5,6] region "folded" back into it. But it only looks that way because the isoceles triangle is symmetrical. If we left the right side (positive frequencies) alone and multiplied the whole left side by 99 (which would require a complex-valued waveform in the time domain), the spectrum of the sampled waveform would no longer look like the [5,6] region "folded" back into the [4,5] region. Rather, it would look like the [-6,-5] region got added directly (i.e., not in reverse order) to the [4,5] region. Nothing got "folded". And indeed, that same explanation works for the symmetrical case. It is the "right" explanation for both cases, because real-valued waveforms are just a special case of complex-valued waveforms (as Nanren said). Folding is just an illusion, generally associated with real-valued waveforms and sampling.
But the Wikipedia article does not say that a real-valued sinusoid at frequency "folds" to frequency It just says there is an image (or "alias") at which is true, because there is the negative one at at and And then it states the simple fact that the common name for this symmetry is "folding". It's just a name, not physics. No doubt there are people who misuse it and/or make incorrect inferences and statements, but wouldn't it be stating the obvious to say that in the article?
-- Bob K 07:36, 1 September 2007 (UTC)
The article says "That effect is known as folding." Many sources describe it that way. If our description is not as good as it should be, then it should be tuned up with respect to one or more reliable sources. If there's a source that says that folding is an incorrect or inadequate view, that should be used and cited as well. Let's get back to what this talk page is for, which is discussing the article, not discussing our own idiosynchratic views.
Dicklyon 16:38, 1 September 2007 (UTC)
Oli, saying that we don't have to resort to negative frequencies is not the same as saying they do not exist. We don't "need" for anything, because it is indistinguishable from However, is a well-defined function. It does exist.
-- Bob K 16:49, 1 September 2007 (UTC)
Can we agree on these points?:
-- Bob K 17:06, 1 September 2007 (UTC)
Evidence of the first point is provided by [5], which states 'Some texts use the term "folding", while others mention this only as "aliasing" '. So why would a textbook avoid mentioning such a widely accepted convention? That would be irresponsible, unless the author has a principled objection to the convention. Rather than editorialize, they simply don't use the flawed convention. If that is the general behavior, then I guess this falls into the category of "can't prove a negative".
-- Bob K 18:41, 1 September 2007 (UTC)
An example of the kind of confusion Nanren is talking about can be found in the new book [1] by renowned author Frederic J. Harris, p 34, Fig 2.27. The "remnants" pointed out in the second of 3 graphs are not mirror images of each other. They bled in from different adjacent channels. But in the third graph, they are shown symmetrically positioned around and the lower one is referred to as a "folded remnant".
-- Bob K 01:09, 2 September 2007 (UTC)
Many thanks for the discussion guys. I liked all the points. Out of interest. (1) I don't think I'm confused about folding. (Maybe that's the worst kind of confusion). (2) I have not run into fred for a LONG time, but he always used to really strongly insist on his name being lower case. (3) On "So why would a textbook avoid mentioning such a widely accepted convention?", good question. Seems there are 3 options, ignore "folding" (for whatever reason), go with "folding" or acknowledge "foldling" & point out the issue, eg that it leads easily to assumptions of completely the wrong mechanisms. I wanted the last one. Can you give me some advice. I like the idea of citing a reference on this topic. The aliasing topic covers a wide area, including many publications, probably none read by all users. Where should the citation be from? Nanren888 06:04, 2 September 2007 (UTC)
Does a poor reconstruction filter actually count as aliasing? No frequency components are being aliased, and it is an invertible process.
In fact, this has already been alluded to above ( #Layman's terms?, #New Intro). Oli Filth( talk| contribs) 20:08, 21 April 2009 (UTC)
- ^ For instance, if the Nyquist-Shannon formula were applied to the samples of it would incorrectly produce
This article is missing any information on my 1991 discovery that I call Super-Nyquist which, using Dan's Aliasing Rules allows you to find the location of an alias for any kind of waveform, sinusoid or complex wave, and an additional discovery by myself and David Reynolds that allows you to determine the true frequency of any aliasing wave using coherent sampling and documented in an article in Evaluation engineering. [1] I also have an article I wrote that fully describes aliasing at [2] and a video that fully describes the technique at YouTube [3] I don't know what the policy is on adding new discoveries to Wikipedia, but I hate to put in all the work of editing this entry and then have it all deleted (as has happened to me before) for not citing peer reviewed articles. Just let it be known that this article is wrong and needs to be rewritten to take my discovery into account. Riverdweller ( talk) 15:14, 24 November 2014 (UTC)
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The point this video is trying to make is better seen in File:AliasingSines.svg. It's simply that when the red sinusoid is undersampled, the samples also match the blue one. Notice also that even when the blue one is properly sampled, the red one is an "alias". Those high-frequency aliases are not shown in the video, even though there is no bandwidth limit on the low-sample-density aliases that are shown. (I.e., the linear interpolations between samples have 1st-derivative discontinuities that require infinite bandwidth.)
The figure caption is If the sampling is not fine enough, the retrieved signal can be very different from the real one. But with no bandwidth limit, it doesn't matter how "fine" is the sampling... the retrieved signal can always be "very different from the real one". The way to fix the video is to replace the linear interpolations with low-frequency sinusoidals, like the blue one in File:AliasingSines.svg. Even so, I don't think the video would add anything that isn't already shown by File:AliasingSines.svg.
-- Bob K ( talk) 14:12, 21 February 2020 (UTC)
For the benefit of less experienced readers, I expanded your file description paragraph, not the figure caption... the one at
https://commons.wikimedia.org/?title=File:FFT_aliasing_600.gif. I hope you don't mind.
--
Bob K (
talk)
13:36, 6 April 2021 (UTC)
"The case shown here is: fcyan = f−1(fgold) = fgold – fs" It looks like the cyan frequency is higher than the gold frequency: The case shown here is: fcyan = f−1(fgold) = fgold + fs" Chris2crawford ( talk) 11:01, 20 June 2024 (UTC)
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I'm not entirely certain what wiki policy is on this, but I've got to assume that any encyclopaedia article should be at least partially understandable by laymen, especially if it's about a topic that directly effects the general public. The reason I ask is that I've seen so many video game reviews (and now DVD review of South Park) which complain about aliasing, and I wish I knew what they were talking about. You'd think that video game reviewers would better explain how aliasing causes problems, but right now, I honestly don't know what the aliasing problems are in my games. - Darkhawk
Ok. You guys don't actually understand what the article says. The word aliasing describes two different but related phenomena. The first is when two different signals are mapped to the same sampled signals (signal->sample is not injective). That is what the smileys were about. The second is about when the signal->sample->reconstruction gives surprising results. That is what the moire patterns in the brick wall are.
Loisel
22:17, 1 March 2007 (UTC)
I wrote probably over half of this article and for a long time I was defending it against non- experts who only have a rudimentary grasp of what aliasing is, but I'm not so sure I care anymore.
Defocusing your lens is again not the same as what the smiley faces represented. Defocusing your lens does not make the pixels big. In fact, you can recover a focused image from a defocused image if you know what you're doing (it's called
deconvolution.) However, you can't recover the smileys from the pixelized image I gave. They're aliased.
Loisel
22:17, 1 March 2007 (UTC)
In statistics, signal processing (including digital photography), computer graphics, and related disciplines, "signals" that are essentially continuous in space or time must be sampled, and the set of samples is never unique to the original signal. The other signals that could (or did) produce the same samples are called aliases of the original signal. If a continuous signal is reconstructed from the samples, the result may be one of the aliases, which represents a form of distortion. The term aliasing can refer to both the ambiguity created by sampling and to the subsequent distortion.
For example, when we view a digital photograph, the reconstruction (interpolation) is performed by our eyes and our brain. If the original image was a lawn, we no longer see the individual blades of grass. Therefore we are seeing an alias. A more interesting example (below) is the Moiré pattern one can observe in a poorly pixelized image of a brick wall. Techniques that avoid such poor pixelizations are called anti-aliasing.
Digital imaging is an example of spatial aliasing. Temporal aliasing is a major concern in the analog-to-digital conversion of video and audio signals: improper sampling of the analog signal will cause high- frequency components to be aliased with genuine low-frequency ones, and to be incorrectly reconstructed as such during the subsequent digital-to-analog conversion. To prevent this problem, the sampling frequency must be sufficiently large and the signals must be appropriately filtered before sampling.
-- Bob K 14:14, 3 March 2007 (UTC)
-- Bob K 15:19, 4 March 2007 (UTC) (revision)
I've taken a stab at a more accessible first sentence, putting the intro more in line with WP:LEDE. ENeville ( talk) 18:28, 28 May 2009 (UTC)
I have an aliasing error versus sampling rate plot taken from Jud Strocks, Telemetry Computer Systems book, I copied. That plot illustrates the RMS error vs sampling rate when using a Butterworh filter with different pole numbers. I would be glad to share it if you want.--Scipio-62 18:49, 23 March 2010 (UTC)
I added this section as a further example that the conventional wisdom of sinc filters isn't always true. Sinc filtering the measured image g, regardless which sinc filter is used, does not lead to any accurate measurement of the radius of the star.
Rnt20 06:37, 11 April 2006 (UTC)
The diameter of Betelgeuse was originally measured in this way. You are incorrect when you say this method was never used to measure the diameter of a star.
Do not remove this example.
Loisel 14:45, 11 April 2006 (UTC)
In my experience, this also happens when watching a spoked wheel. Can someone confirm? (or is this maybe evidence that I'm living in the Matrix... hm, my head hurts now ;-) -- Tarquin 15:26 Dec 20, 2002 (UTC)
This could be the case if your eye samples the scene - perhaps periferal vision does this. I sometimes get a related effect if I see a TV screen or other flickering source out of the corner of my eye - the flicker frequency appears to be much less than 50Hz. -- Easter 15:32 Dec 20, 2002 (UTC)
For really freaky effects, try watching a TV screen or CRT monitor while using an electric toothbrush. The image wobbles up and down, it was quite alarming the first time I saw it. -- Tarquin
This is what my colleagues in broadcast engineering call the ginger biscuit effect. Any vibration to the head will do. -- Easter 15:47 Dec 20, 2002 (UTC)
I think we need an article on this! -- Tarquin
This effect is caused by a failure of persistence of vision, although it could also be regarded as a kind of aliasing (with the vibration of your head providing the sampling frequency). I don't believe that the eye normally does any sampling in the time domain, at least not in a periodic way. Devices like CRT monitors rely on your persistence of vision, which is the slow response of your retina to changing or flickering images. This only works if your eye muscles can produce a stationary image on the retina. When you move your head faster than your eye muscles can track, as happens when you eat crunchy food, the TV image is spread out over your retina and appears fragmented, because parts of your retina see one field of the image and other parts see the next field, or the few milliseconds of darkness between fields. I'm guessing that this effect is more noticeable at the edge of the field of view, because the mechanism that stabilises the eyeball mainly uses data from the centre of the retina. -- Heron 11:30, 31 Mar 2004 (UTC)
I agree -- we need an article on this! What to call it? Recently I've heard it called the "Dorito effect", but Google Fight tells me that "Frito effect" is far more popular. Or is there some other name that would be better for a "serious" (?) encyclopedia article? -- DavidCary 07:13, 14 October 2005 (UTC)
The Frito Effect the Frito Effect Aliasing - A new perspective
Maybe this isn't exactly the same effect, but the most compelling example of this kind of phenomenon I have ever seen occurs when in a dark room, viewing one of those old digital alarm clocks with the red numbering (search for "digital alarm clock" in google images - first few examples are what I'm talking about) just off center, and moving your head around quickly... not violently fast, but fairly fast. The image of the numbers will appear to not be able to keep up with the physical clock, and drift off it to the left and right, up and down, pretty fair distances if you do it just right. —Preceding unsigned comment added by 66.31.7.121 ( talk) 02:51, 3 February 2008 (UTC)
This article has a See Also to
Wagon-wheel_effect, which links to
Temporal aliasing, which is re-directed back to here. Here we point out that sin(-wt+θ) = sin(wt-θ+π) = cos(wt-θ+π/2). So I'm curious why our brain perceives the wheel rotating backward (analogous to sin(-wt+θ)) instead of forward. Most optical illusions, such as the
Ames window and
Ames room occur when our brain tries too hard to interpret what it sees in terms of what it already knows, such as rectangular windows and wagon wheels rotating in the forward direction.
-- Bob K ( talk) 15:43, 7 March 2012 (UTC)
OK, so far, so mathematical, but the article now uses no fewer than four different kinds of L: can the sampling mappings please be called something different, to avoid confusion?
That's ok, but I'm not sure that attempt is optimal. Perhaps and or would be better. You have to be careful to change all the references to and if you do that, they are used consistently throughout the article. I'm going to wait and watch, but if you want me to do it, and have a notation suggestion, just let me know here. Loisel 00:40 Jan 28, 2003 (UTC)
I have a question regarding this paragraph:
The term "aliasing" derives from the usage in radio engineering, where a radio signal could be picked up at two different positions on the radio dial in a superheterodyne radio: one where the local oscillator was above the radio frequency, and one where it was below. This is analagous to the frequency-space "wrapround" that is one way of understanding aliasing. However, there is a deeper way of understanding aliasing, based on continuity arguments, which is outlined below as an introduction.
This is very interesting to me. I am not completely certain that this crosstalk between radio stations is covered by the "outlined below as an introduction" portion. Unfortunately, I am not a physicist (or an engineer) so I don't know what's actually going on.
I think it would be great if someone who understands the long-winded L^2 stuff I wrote could tell me how that relates to the radio waves. I mean, the wrapping around of frequencies I describe depends completely on using a simple sampling scheme (like S_0) and so it's mostly for digital signal processing. In the analog world, I'm not exactly sure what's going on.
If anyone can give us more details about the underlying physics of the radio wave crosstalk phenomenon described above, perhaps there's a section in the aliasing article that needs to treat the analog aliasing process separately, which might be different from the dsp aliasing stuff Loisel 01:38 Jan 28, 2003 (UTC)
The subsection numbers under "technical discussion" serve a purpose: the introduction to "technical discussion" refers to these sections by number. If you want to remove the subsection numbers, you'll have to change the introduction as well. For reference purposes, Encyclopedia Britannica uses numbering for some of its articles (my 1973 copy of World Wars has a complicated numbering system.) Loisel 18:49 Jan 28, 2003 (UTC)
I'm referring to this: In engineering, the method introduced in the third section is called sampling, while a method such as that introduced in the fifth section is called filtering. This discussion may be viewed as a theoretical introduction to the ideas of anti-aliasing. Loisel 18:51 Jan 28, 2003 (UTC)
An article titled "Bishop", after hundreds of words on concept of "bishop" used in religion, had a one-line comment that a piece in chess is called a "bishop", with an appropriate link. I moved that to the beginning of the article where it would actually be seen be anyone interested. I've done the same thing here with the meaning of "aliasing" in computer science. Michael Hardy 19:18 Jan 28, 2003 (UTC)
Hfastedge, don't pollute carefully written articles with your requests. That's what the talk page is for. Loisel 07:29 30 Jun 2003 (UTC)
WHAT THE HELL HAPPENED? Loisel 17:55, 29 Jul 2003 (UTC)
What's this 4LIQ9nXtiYFPCSfitVwDw7EYwQlL4GeeQ7qSO business? Evercat 17:59, 29 Jul 2003 (UTC)
Please don't use <math> in headers. Use a proper substitution. —Eloquence 18:01, 29 Jul 2003 (UTC)
Can someone fix the mathematic notations in the article?
What we need is ONE simple picture showing a sinusoid being sampled at too high rate and matching a lower-frequency sinusoid. Then we can probably delete some 10,000 words... Jorge Stolfi 20:46, 23 Mar 2004 (UTC)
The picture added is good for understanding the time domain aspect of aliasing. However, the reconstruction distortions are based on frequency domain filtering. I'm going to try to find a good picture for that. Mojodaddy 05:22, 20 December 2006 (UTC)
I found a good one, it's found here as the lower picture: http://efunda.com/designstandards/sensors/methods/DSP_Aliasing.cfm?search_string=aliasing It's far more insightful than the current discrete frequency picture. If someone could replicate something similar to that, that'd be awesome. 130.85.235.240 22:29, 21 December 2006 (UTC)
The "Technical description" section was way too long and too heavy on math, it confused more than clarified the concept. Thus I have done some rather radical trimming and replanting.
Specifically, I moved most details of the "reconstruction" sections to a new page signal reconstruction, keeping only the definition of the "standard" reconstruction R. I also deleted the following paragraph since it was not germane to "aliasing"; it should go to some other page (Fourier analysis?):
The following paragraph was deleted too; perhaps it should go to signal processing:
The following paragraphs did not seem to make sense: given that "signal" was defined as a *function*, it would seem that is always well-defined in that case. Perhaps this text was assuming that a signal could be a *distribution* (such as, e.g., Dirac's)?
The following section has the same problem, and it also assumes non-trivial concepts of wavelets etc., so it should probably go elsewhere, too:
Finally the discussion of the operator does not seem to be very useful. The operator does not eliminate aliasing, it only reduces it. On the other hand, when addressing this topic one MUST discuss the sinc filter (which does eliminate aliasing) and the Gaussian filter (which does a pretty good job, and is free from ringing). In any case, this material should be in anti-aliasing, not here.
Jorge Stolfi 01:55, 25 Mar 2004 (UTC)
The sound example needs more explanation: what is the sampling rate, what exactly is meant by "bandlimited", and what should the listener pay attention to. Jorge Stolfi 18:43, 24 Mar 2004 (UTC)
Having specifically said that the Nyquist condition is simplistic, I don't think the following theory adequately explains why this is the case. I mean, it may explain it, but it doesn't specifically summarize why it is that the Nyquist criterion is therefore simplistic. I don't think readers should have to dig so much, only to find vague statements under caveats -- Tlotoxl 10:15, 31 Mar 2004 (UTC)
Shouldn't there be a mention about aliasing in TV broadcast? The reason why moderators don't have certain patterns of dress and so on. Just a thought. 84.42.132.48 11:31, 1 September 2005 (UTC)
Right at the start of the article, where it says:
shouldn't that be analog-to-digital not digital-to-analog or am I just confused?
This paragraph seems to by trying to say that aliasing occurs when you sample analog to digital. It says improper sampling of the analog signal will cause... That seems to imply that analog is the source in this paragraph.
It seems confusing as written, someone who knows better please help me understand this. HighInBC 18:12, 27 February 2006 (UTC)
Thanks. HighInBC 23:58, 27 February 2006 (UTC)
Can someone explain the new animated example. It seems way too busy and confusing. Do we really need animation for this? Can it be explained with some commentary at least? I'm going to take it out for now. Please comment if you like it, or put it back with commentary, or make a more accessible example. Dicklyon 02:44, 4 July 2006 (UTC)
Hi! I believe that is really useful and powerful, though I think there is a small mistake. If we see one single gif frame, we can clearly understand that the main common frequency of all the plotted components is 0.5Hz =30rpm (assuming that the sampling rate is correct). But the title clearly states that the cam-follower is running at 200rpm (which doesn't have much to do with 30rpm). Therefore, either I'm missing something or there is a mistake somewhere. —Preceding unsigned comment added by 93.56.195.203 ( talk) 17:23, 30 April 2011 (UTC)
Apparently I've made no progress getting Rbj to understand the notion of mathematical implication, and the difference between a provably true theorem and its not-always-true converse. He has come over here to spread his joy, having "crapped up" (his words) the Nyquist–Shannon sampling theorem article in the last day or two. He has a narrow view of aliasing based on baseband reconstruction, which he is also mixing up with the notion of an alias itself. My changes are individually documented to indicate the errors in what he has done. Dicklyon 15:43, 17 August 2006 (UTC)
I don't thing there's a lot of point having a separate article for this that contains three sentences, all of which are already implied by the content of this article. Any reason not to just redirect it to here and remove the link from this article? JulesH 09:56, 21 November 2006 (UTC)
Done. I hope you're OK with it, CB. Dicklyon 05:55, 23 January 2007 (UTC)
The POV "ancillary comment" about that linked PDF sounds like something I may have written in my early wikipedia days; if so, it sure lasted a long time, but you're right it sure doesn't belong. Anyway, specific complaints about the Lavry PDF include:
So, now that the disclaimer is gone, I think I'll remove the ext link, too. Dicklyon 21:38, 22 January 2007 (UTC)
Bob K had updated first paragraph to say:
Several problems here. It is ALWAYS true that , the way he defined it, but the text can appear to be saying that is the smallest; it's unclear if this was intended, or is just an incorrect reading of it, but it's confusing.
Dicklyon
19:15, 28 February 2007 (UTC)
And if this was patched up, the "(and only if)" bit is still incorrect, unless you go to the trouble of separately excluding f at the Nyquist frequency.
But it seems to me that this change is not well motivated. The way it's stated now makes the "folding" or "mirroring" property of aliasing more explicit. The folded term is the usual main term that you need to care about, and the absolute value obscures more than clarifies, I think.
Dicklyon
19:15, 28 February 2007 (UTC)
In my opinion, the section on subsampling a sinusoid is really unclear and poorly done. — Preceding unsigned comment added by 137.53.91.144 ( talk) 21:51, 23 February 2012 (UTC)
In section 5.1, we have:
In section 5.6, we conclude with:
In case it isn't obvious, I think what we are saying is that an anti-aliasing filter (and a rectangular one at that) is a good thing to do before sampling.
But how do we confine a sinc function to the interval [0,1]? Is that why we need the "some sort of" caveat? And how do we design a "sort of sinc" filter?
Frankly, these sections don't do much for me. Why "teach" functional analysis here? The relevant points seem to be these:
Am I missing something? Are these unsurprising (and in some cases vague) points enough to justify section 5?
-- Bob K 14:18, 10 March 2007 (UTC)
I think this section may be largely incorrect, or at least somewhat wide of the mark. In my recollection, and what few revelant refs I've been able to find, an alias in radio is just am image frequency. Most of the discussion about spectrum reversal seems not quite relevant. The point of aliasing is not so much that you have a choice of high-side or low-side local oscillator, but that after you've chosen you still have to fight the image or alias from the other side. Is there a book that either makes this clear or supports the current text? Dicklyon 16:58, 18 March 2007 (UTC)
I added the "expert needed" tag. I used to keep an eye on this page but I have stopped and there's some nonsense in there now, but I don't have time to take care of it. I hope the current editors do find an expert. Loisel 01:46, 21 June 2007 (UTC)
Hello again. Some random comments:
Did you intend to keep both of these redundant statements?:
The sun example that you removed predates my involvement. I just fixed it up a bit. I am sorry to see it go away, but no biggie. However, removing it also removes the reason for introducing the symbol so early in the article. Consider postponing its introduction until it is needed.
And it also removes the concept of negative frequency (like a wagon wheel going backward). So now the statement: "And the concept of negative frequency is not necessary, because there is always an identical sinusoid with a positive frequency..." just appears out of nowhere. But I would not advise removing the concept of negative frequency. I think it is useful and interesting to make the point that some phenomena, such as sun motion and wagon wheels and complex sinusoids, are directional and require signed frequency, but real-valued sinusoids do not.
-- Bob K 13:02, 21 June 2007 (UTC)
Ok, well known, but incorrect. No way can I go with folding over negative frequency. Putting people on completely the wrong track is not better than telling the truth, even if the truth takes a little more work to get clear. I'll read up on how Wikipedia & editing works, but I added a comment to this effect today & had it removed by Oli Filth. Sorry mate, wrong. Improve it by all means, but there is no mechanism for "folding" & we should no proliferate the misunderstanding. As I said, I'll try to make time to learn enough to do the job properly, but maybe one of you guys who do this all the time could just deal to the "folding" thing & set it straight to save me the trouble. —Preceding unsigned comment added by Nanren888 ( talk • contribs) 07:48, 31 August 2007 (UTC)
I am bound to repeat some points already made above, but for what it's worth:
Consider a Fourier transform shaped like an isoceles triangle with its peak at 0 Hz and a base width (two-sided) of 12 Hz (i.e., ±6 Hz). Now sample the waveform at Hz. In the region between 4 Hz and 5 Hz (), it looks like the [5,6] region "folded" back into it. But it only looks that way because the isoceles triangle is symmetrical. If we left the right side (positive frequencies) alone and multiplied the whole left side by 99 (which would require a complex-valued waveform in the time domain), the spectrum of the sampled waveform would no longer look like the [5,6] region "folded" back into the [4,5] region. Rather, it would look like the [-6,-5] region got added directly (i.e., not in reverse order) to the [4,5] region. Nothing got "folded". And indeed, that same explanation works for the symmetrical case. It is the "right" explanation for both cases, because real-valued waveforms are just a special case of complex-valued waveforms (as Nanren said). Folding is just an illusion, generally associated with real-valued waveforms and sampling.
But the Wikipedia article does not say that a real-valued sinusoid at frequency "folds" to frequency It just says there is an image (or "alias") at which is true, because there is the negative one at at and And then it states the simple fact that the common name for this symmetry is "folding". It's just a name, not physics. No doubt there are people who misuse it and/or make incorrect inferences and statements, but wouldn't it be stating the obvious to say that in the article?
-- Bob K 07:36, 1 September 2007 (UTC)
The article says "That effect is known as folding." Many sources describe it that way. If our description is not as good as it should be, then it should be tuned up with respect to one or more reliable sources. If there's a source that says that folding is an incorrect or inadequate view, that should be used and cited as well. Let's get back to what this talk page is for, which is discussing the article, not discussing our own idiosynchratic views.
Dicklyon 16:38, 1 September 2007 (UTC)
Oli, saying that we don't have to resort to negative frequencies is not the same as saying they do not exist. We don't "need" for anything, because it is indistinguishable from However, is a well-defined function. It does exist.
-- Bob K 16:49, 1 September 2007 (UTC)
Can we agree on these points?:
-- Bob K 17:06, 1 September 2007 (UTC)
Evidence of the first point is provided by [5], which states 'Some texts use the term "folding", while others mention this only as "aliasing" '. So why would a textbook avoid mentioning such a widely accepted convention? That would be irresponsible, unless the author has a principled objection to the convention. Rather than editorialize, they simply don't use the flawed convention. If that is the general behavior, then I guess this falls into the category of "can't prove a negative".
-- Bob K 18:41, 1 September 2007 (UTC)
An example of the kind of confusion Nanren is talking about can be found in the new book [1] by renowned author Frederic J. Harris, p 34, Fig 2.27. The "remnants" pointed out in the second of 3 graphs are not mirror images of each other. They bled in from different adjacent channels. But in the third graph, they are shown symmetrically positioned around and the lower one is referred to as a "folded remnant".
-- Bob K 01:09, 2 September 2007 (UTC)
Many thanks for the discussion guys. I liked all the points. Out of interest. (1) I don't think I'm confused about folding. (Maybe that's the worst kind of confusion). (2) I have not run into fred for a LONG time, but he always used to really strongly insist on his name being lower case. (3) On "So why would a textbook avoid mentioning such a widely accepted convention?", good question. Seems there are 3 options, ignore "folding" (for whatever reason), go with "folding" or acknowledge "foldling" & point out the issue, eg that it leads easily to assumptions of completely the wrong mechanisms. I wanted the last one. Can you give me some advice. I like the idea of citing a reference on this topic. The aliasing topic covers a wide area, including many publications, probably none read by all users. Where should the citation be from? Nanren888 06:04, 2 September 2007 (UTC)
Does a poor reconstruction filter actually count as aliasing? No frequency components are being aliased, and it is an invertible process.
In fact, this has already been alluded to above ( #Layman's terms?, #New Intro). Oli Filth( talk| contribs) 20:08, 21 April 2009 (UTC)
- ^ For instance, if the Nyquist-Shannon formula were applied to the samples of it would incorrectly produce
This article is missing any information on my 1991 discovery that I call Super-Nyquist which, using Dan's Aliasing Rules allows you to find the location of an alias for any kind of waveform, sinusoid or complex wave, and an additional discovery by myself and David Reynolds that allows you to determine the true frequency of any aliasing wave using coherent sampling and documented in an article in Evaluation engineering. [1] I also have an article I wrote that fully describes aliasing at [2] and a video that fully describes the technique at YouTube [3] I don't know what the policy is on adding new discoveries to Wikipedia, but I hate to put in all the work of editing this entry and then have it all deleted (as has happened to me before) for not citing peer reviewed articles. Just let it be known that this article is wrong and needs to be rewritten to take my discovery into account. Riverdweller ( talk) 15:14, 24 November 2014 (UTC)
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The point this video is trying to make is better seen in File:AliasingSines.svg. It's simply that when the red sinusoid is undersampled, the samples also match the blue one. Notice also that even when the blue one is properly sampled, the red one is an "alias". Those high-frequency aliases are not shown in the video, even though there is no bandwidth limit on the low-sample-density aliases that are shown. (I.e., the linear interpolations between samples have 1st-derivative discontinuities that require infinite bandwidth.)
The figure caption is If the sampling is not fine enough, the retrieved signal can be very different from the real one. But with no bandwidth limit, it doesn't matter how "fine" is the sampling... the retrieved signal can always be "very different from the real one". The way to fix the video is to replace the linear interpolations with low-frequency sinusoidals, like the blue one in File:AliasingSines.svg. Even so, I don't think the video would add anything that isn't already shown by File:AliasingSines.svg.
-- Bob K ( talk) 14:12, 21 February 2020 (UTC)
For the benefit of less experienced readers, I expanded your file description paragraph, not the figure caption... the one at
https://commons.wikimedia.org/?title=File:FFT_aliasing_600.gif. I hope you don't mind.
--
Bob K (
talk)
13:36, 6 April 2021 (UTC)
"The case shown here is: fcyan = f−1(fgold) = fgold – fs" It looks like the cyan frequency is higher than the gold frequency: The case shown here is: fcyan = f−1(fgold) = fgold + fs" Chris2crawford ( talk) 11:01, 20 June 2024 (UTC)