Well, not having ever taken the time to compute ƒ(meow) I couldn’t tell you how close the approximation in the graphic really is, but it’s plausible. (Damn WordPress doesn’t have a decent Fourier transform operator symbol…)
Believe me when I say that the Fourier transform of my morbidly obese cat Jilly is the kindest and thinnest way I think we’ll ever witness her.
Below is the continuous Fourier transform in the general Euler form rather than the cosine/sine variation for even/odd functions that are initially easier to look at when trying to make sense of the whole thing. If you took the transform of Jilly in the very most flattering light (basically a roundish DC signal) you’ll get a delta at zero frequency – razor thin. She’s actually more of a long-ish single rectangular pulse so her transform will be sort of a central peak – but kind of spread out and lumpy, so I guess you could say she’s already been transformed.
Note #2: But by gum it works and it holds water after all this time. Euler is one of my heroes, right behind Feynman. Ask Cruel Wife, she’ll tell you. Granddad was #1.