Fourier
Fourier
[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!

A Fourier transform is a mathematical function transformation 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 and amplitudes. (The most obvious application is in analyzing 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. This can be done by evaluating an integral based on the function, which is referred to as "taking the Fourier transform" of the function. The form of the integral that needs to be taken 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.
[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!
