[BW] For mathematical cat lovers

If you love math, as well as cats, you might get a grin out of this
web comic:

jXwXeXrXmXoXnXt...

As someone with a bachelor's degree in math, I am deeply embarrassed to
have to ask: what is a Fourier transform? Either I didn't learn this, or,
even worse, I did learn it and have completely forgotten it.

Takayuki...

I wouldn't worry about it. Most people I know who know Fourier
transforms didn't learn it in school, but picked it up on the job,
because it happened to be necessary for their work. I've known
salespeople who could speak intelligently about FT algorithms because
they make their living selling PC boards that do Fourier transforms.

William Hamblen...

Fourier showed that a function could be expressed as sums of
sines and cosines. The function of amplitude vs. frequency that
results is the fourier transform of the original function. You
can do an inverse fourier transform to get back the original
function. I don't see why the guy in the cartoon didn't try
that. :)

jXwXeXrXmXoXnXt...

LOL. Is there anything lost when you do that, though? Like when you
find the derivative of a function, and then perform the integral, you
don't exactly get the original back. You get the curve, but it's not
clear where to place it. :) (Hey, at least I remember something!)

Dan M...

It's been a while since I've done any DSP, so I'm working from foggy
memory here, but as long as the data sampling meets the Nyquist sampling
criterion then the data that's reconstructed from the Fourier transform
will have fairly low error. Not zero error, though.

jXwXeXrXmXoXnXt...

Not zero, eh? Might be a bit tough on a Fourier-transformed kitty, then! :)

Dan M...

Yeah - a tortie might come out as a calico :)

Discrete Fourier Transforms can be done using complex numbers or real
numbers. Complex datasets will yield closer approximations.

I guess I really ought to break out some of my old textbooks and play with
DFT and FFT again. I've forgotten almost everything I used to know about
it!

annoyed...

Ugh. Fourier, Laplace and Z Transforms bring back nightmares from Network
Synthesis classes at DeVry - Cauer and Chebyshev filters - *shudder* :O

Or like when you scale down an image, and then scale it back up -
whoops, the resolution's not so great anymore. (Depends on the
scale-down algorithm, of course.)

William Hamblen...

You can an infinite series out of the transform, which means in

jXwXeXrXmXoXnXt...

Sorry, don't mean to be the writing police, but you seemed to have left
the verb out of the above sentence. And I think it must be an important
part of the sentence, because I'm not sure what the word should be. Is
it "create"?

real life you can't do it, but when has that stopped
mathematicians?

jXwXeXrXmXoXnXt...

One of the things I like about math.

They teach engineers about fourier transforms. It shows up in
signal processing.

Pat...

Don't be embarrassed, it is PhD-level stuff.

Chakolate...

LOL! Oh, that is too sick. I love it.

Since the first class I will be taking as I go back to school (after 24.5
years out of school) is math.... *WAY* over my head.

But I *did* like this one:

I'll have a bowl of Frosted Bacon Flakes, please LOL