[BW] For mathematical cat lovers

Mark Edwards wrote:

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

http://xkcd.com/c26.html

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.

Joyce

wrote

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.

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

wrote:
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.

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.

wrote:
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.

http://en.wikipedia.org/wiki/Fourier_transform

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On 2006-09-06, wrote:

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.

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.

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

Bud

William Hamblen wrote:

On 2006-09-06, wrote:

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.

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.

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!)

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.)

Joyce

Victor Martinez wrote:

wrote:
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.

http://en.wikipedia.org/wiki/Fourier_transform

Thanks, Victor. That will be a lot more informative once I'm fully
awake.

Joyce

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!)

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.

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!

Dan

Dan M wrote:

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!)

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.

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

Joyce

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

Joyce

Yeah - a tortie might come out as a calico