
Ask HN: Who was Joseph Fourier? - poseid
Of course, Wikipedia tells us Joseph Fourier lived 1768 until 1830, but what I don&#x27;t understand is how could he invent the tools that are so important in digital signal processing today?
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yorwba
For his analytic theory of heat, he was working with differential equations to
express heat propagation.

Those equations are especially easy when applied to trigonometric functions
like sine and cosine (because their derivates are easy to express in terms of
each other).

He didn't really have a way to solve the equations for other functions
directly, but he tried to approximate them by sums of trigonometric functions.
He noticed that he could actually do that for all functions he wanted to
analyze, and wrote about that in his book.

Later, other mathematicians qualified the circumstances that make such a
transformation possible, formally proved its properties and named it "Fourier
transform" in his honor.

Because of its applicability to problems involving differential equations, the
Fourier transform was also used in other domains of physics e.g. to analyze
vibrations like sound.

Because of those many uses, people needed a way to compute it quickly, so they
optimized the algorithm to create the Fast Fourier Transform.

So those "tools that are so important in digital signal processing today" were
not invented by Fourier singlehandedly, but are associated with his name due
to him kicking off the initial development.

Actually, Gauss used a variant of the FFT in his astronomical work even before
Fourier published his own results, but because Gauss didn't publish, he is not
associated with the discovery.

~~~
poseid
thanks, i see... i read about travels to Egypt, and then curiosity on heat
transport. back in that time, heat was understood differently than today, but
interesting to see how the fluctuations in temperature of day/night of
month/year follow a bit of sinusoidal pattern indeed. do you recall what those
basic heat equations were back in that time, and why it was different from
theories back then? just in case you have some more time to write on this....
thanks!

~~~
yorwba
The Wikipedia article on the heat equation has a section on using Fourier
series:
[https://en.wikipedia.org/wiki/Heat_equation#Solving_the_heat...](https://en.wikipedia.org/wiki/Heat_equation#Solving_the_heat_equation_using_Fourier_series)

I assume that except for the adaptation to modern notation, the general idea
of the argument has been preserved.

Note that sinusoids are only used because they make the calculations
convenient, and not because of the day/night cycle or actual sinusoidal heat
distributions empirically observed in nature.

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samfisher83
[https://en.wikipedia.org/wiki/George_Boole](https://en.wikipedia.org/wiki/George_Boole)

George boole lived in 18th century. He came up with boolean algebra which is
used extensively in digital circuits.

Euler, Newton, and Gauss all lived from 16th - 18th century and they are
responsible for a large chunk of the math we have today which a reason we have
computers.

We stand on the shoulder of giants.

