# 26: Fourier

(→Explanation: a bit more explanation on the transform) |
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==Transcript== | ==Transcript== | ||

− | :[Cueball talks on phone. | + | :[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! |

## Revision as of 15:50, 22 May 2014

Fourier |

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

- Original comments from Randall: "I like the idea of a graph meowing. Also, that cat has a lot of periodic components."
- This is the twenty-seventh comic originally posted to livejournal. The previous was 25: Barrel - Part 4. The next was 27: Meat Cereals.

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# 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

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