Difference between revisions of "26: Fourier"

Explain xkcd: It's 'cause you're dumb.
Jump to: navigation, search
m (fixed grammatical errors)
(6 intermediate revisions by 4 users not shown)
Line 10: Line 10:
 
A {{w|Fourier transform}} is a mathematical function often used in physics and engineering.
 
A {{w|Fourier transform}} is a mathematical function often used in physics and engineering.
  
The theory is that any line graph can be represented as the sum of a bunch of sine waves of different frequencies, with each frequency having a different amplitude. (The most obvious application is in analysing a sound recording in terms of the different frequencies of sounds used.) So, for any line graph you can produce another graph of the frequencies and their amplitudes. To do this, there is a function where you put in one graph and you get the second graph as output, and this process of going from one to the other is a "transform". This function is actually shown in the third line of the comic [[55: Useless]].  
+
The theory is that any line graph can be represented as the sum of a bunch of sine waves of different frequencies, with each frequency having a different amplitude. (The most obvious application is in analysing a sound recording in terms of the different frequencies of sounds used.) So, for any line graph, you can produce another graph of the frequencies and their amplitudes. To do this, there is a function where you put in one graph and you get the second graph as output, and this process of going from one to the other is a "transform". This function is actually shown in the third line of the comic [[55: Useless]].  
  
Unfortunately Cueball has applied this "transform" to his cat...
+
Unfortunately, Cueball has applied this "transform" to his cat. Although it seems to still be alive and possibly even unharmed, it is clearly not in its familiar shape, and it is not clear if this condition is permanent or not.
  
 
"Periodic components" in the title text refers to the spikes in the graph.  Because sine waves repeat themselves as you go along, the presence of large amounts of one particular sine wave in the Fourier transform graph (each spike) shows that the overall result (the initial graph) is likely to have parts that also repeat themselves, like a {{w|periodic function}}. In other words, the cat has repeating parts.
 
"Periodic components" in the title text refers to the spikes in the graph.  Because sine waves repeat themselves as you go along, the presence of large amounts of one particular sine wave in the Fourier transform graph (each spike) shows that the overall result (the initial graph) is likely to have parts that also repeat themselves, like a {{w|periodic function}}. In other words, the cat has repeating parts.
  
 
==Transcript==
 
==Transcript==
:[Cueball talks on phone. Cat with many sharp points looks on.]
+
:[Cueball talks on phone. A grotesque-looking cat with many sharp vertical points looks on.]
 
:Cueball: Hi, Dr. Elizabeth?  Yeah, uh ... I accidentally took the Fourier transform of my cat...
 
:Cueball: Hi, Dr. Elizabeth?  Yeah, uh ... I accidentally took the Fourier transform of my cat...
 
:Cat: Meow!
 
:Cat: Meow!
  
 
==Trivia==
 
==Trivia==
*Original comments from [[Randall]]: "I like the idea of a graph meowing. Also, that cat has a lot of periodic components."
+
*This was the 27th comic originally posted to [[LiveJournal]].
*This is the twenty-seventh comic originally posted to livejournal. The previous was [[25: Barrel - Part 4]]. The next was [[27: Meat Cereals]].
+
**The previous was [[25: Barrel - Part 4]].  
 +
**The next was [[27: Meat Cereals]].
 +
*Original title: "Wednesday's Drawing - Fourier"
 +
*There were no original [[Randall]] quote for this comic.
 +
*This comic was posted on [[xkcd]] when the web site opened on Sunday the 1st of January 2006.
 +
**It was posted along [[:Category:First day on xkcd|with all 41 comics]] posted before that on LiveJournal as well as a few others.
 +
**The latter explaining why the numbers of these 41 LiveJournal comics ranges from 1-44.
 +
*One of the original drawings drawn on [[:Category:Checkered paper|checkered paper]].
  
 
{{comic discussion}}
 
{{comic discussion}}
[[Category:Comics posted on livejournal]]
+
 
 +
[[Category:Comics posted on livejournal| 27]]
 +
[[Category:First day on xkcd]]
 +
[[Category:Checkered paper]]
 +
[[Category:Comics with color]]
 
[[Category:Comics featuring Cueball]]
 
[[Category:Comics featuring Cueball]]
 
[[Category:Math]]
 
[[Category:Math]]
 +
[[Category:Animals]]

Revision as of 14:52, 20 June 2017

Fourier
That cat has some serious periodic components
Title text: That cat has some serious periodic components

Explanation

A Fourier transform is a mathematical function often used in physics and engineering.

The theory is that any line graph can be represented as the sum of a bunch of sine waves of different frequencies, with each frequency having a different amplitude. (The most obvious application is in analysing a sound recording in terms of the different frequencies of sounds used.) So, for any line graph, you can produce another graph of the frequencies and their amplitudes. To do this, there is a function where you put in one graph and you get the second graph as output, and this process of going from one to the other is a "transform". This function is actually shown in the third line of the comic 55: Useless.

Unfortunately, Cueball has applied this "transform" to his cat. Although it seems to still be alive and possibly even unharmed, it is clearly not in its familiar shape, and it is not clear if this condition is permanent or not.

"Periodic components" in the title text refers to the spikes in the graph. Because sine waves repeat themselves as you go along, the presence of large amounts of one particular sine wave in the Fourier transform graph (each spike) shows that the overall result (the initial graph) is likely to have parts that also repeat themselves, like a periodic function. In other words, the cat has repeating parts.

Transcript

[Cueball talks on phone. A grotesque-looking cat with many sharp vertical points looks on.]
Cueball: Hi, Dr. Elizabeth? Yeah, uh ... I accidentally took the Fourier transform of my cat...
Cat: Meow!

Trivia

  • This was the 27th comic originally posted to LiveJournal.
  • Original title: "Wednesday's Drawing - Fourier"
  • There were no original Randall quote for this comic.
  • This comic was posted on xkcd when the web site opened on Sunday the 1st of January 2006.
    • It was posted along with all 41 comics posted before that on LiveJournal as well as a few others.
    • The latter explaining why the numbers of these 41 LiveJournal comics ranges from 1-44.
  • One of the original drawings drawn on checkered paper.


comment.png add a comment! ⋅ comment.png add a topic (use sparingly)! ⋅ Icons-mini-action refresh blue.gif refresh comments!

Discussion

Isn't the cat also imaginary because its Fourier transform isn't symmetric?

I feel like there's another joke in that his cat is "imaginary" or has complex components.

Shdwdrgn (talk) 06:33, 8 October 2014 (UTC)shdwdrgn

Picking up on shdwdrgn's comment above, how interesting would the Fourier transform of Schroedingers's cat be. I guess it would consist of two overlaid graphs neither of which would be certain until you actually looked at it.EditorGonk (talk) 09:38, 20 July 2018 (UTC)


Might this also be a Garfield joke? Garfield's veterinarian is named Liz. Although Garfield, being roughly a three-dimensional ovoid, would probably end up with a much different looking Fourier transform than what is depicted here.

--199.27.130.246 21:26, 9 October 2014 (UTC)

I think the transform may be of the movements of various parts of the cat. Cats tend to move their ears and heads a lot, and other parts, less so. What tipped me off is the spike at the tip of the tail. Cats typically twitch the very tip of their tail in a rhythmic fashion. 108.162.216.192 21:52, 2 March 2015 (UTC)

Coincidentially, the Fourier transform of a cat was used in a 2003 paper on the so-called phase problem in protein crystallography (figure 3) to illustrate the relevance of phase and amplitude information. See http://journals.iucr.org/d/issues/2003/11/00/ba5050/index.html and http://journals.iucr.org/d/issues/2003/11/00/ba5050/ba5050fig3.html

Can someone do a reverse fourier transform on the cat's graph and post it here please? --162.158.79.37 18:12, 14 July 2020 (UTC)Bumpf