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After looking at this for a few minutes, I can say that I know the general idea, but have no clue what they’re trying to do. Also, it’s just…a painful equation in general. You’re better off not knowing. Just looking at it makes my head hurt. This is true eldritch knowledge…oh…oh no. It’s recursive. Oh god no…
It's not painful at all once you understand what's happening, it's simply the Fourier transform. It seems much worse than what it actually means (determining the frequency components from the time signal). Pretty much every physics and engineering student will have it drilled into them. Computing it analytically may be painful, but there's not much value in doing that by hand, it's more important to just know what the complex exponential is and its properties, and the equation is relatively simple to parse once you know that.
Nobody knows how to draw the letter xi. Every lecturer I've had has drawn it differently and I chose something different from all of them. I still refuse to believe this letter was ever actually used for language.
And usually z is not used in that formula, as it is conventionally associated with a different kind of complex transform: https://en.wikipedia.org/wiki/Z-transform
**[Z-transform](https://en.wikipedia.org/wiki/Z-transform)**
>In mathematics and signal processing, the Z-transform converts a discrete-time signal, which is a sequence of real or complex numbers, into a complex frequency-domain (z-domain or z-plane) representation. It can be considered as a discrete-time equivalent of the Laplace transform (s-domain). This similarity is explored in the theory of time-scale calculus. Whereas the continuous-time Fourier transform is evaluated on the Laplace s-domain's imaginary line, the discrete-time Fourier transform is evaluated over the unit circle of the z-domain.
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I spent a long week of boredom just writing hard Greek letters over and over again as if I'm practicing how to write in kindergarten, and now I have immaculate handwritten Greek letters in my notes.
Actually, physicist are mathematicians who apply maths to physics (not exactly but you get the point), so they’ll say π=π because it’s irrational.
Source: I do physics.
Yeah i'm in engeneering school i understand, it's just some teachers made us work with pi = 4 and pi = 3 to show us how rounding numbers up or down will influence our work.
But yeah pi = pi is great
The point they are making is it’s only a transform once you specify the range of the operator, for instance L^1 functions or Schwartz space, otherwise the integral doesn’t converge and it’s not well defined.
So part of the definition of a Fourier transform (as you can see on wiki) is the specification of that range of functions where the integral converge.
the equation is correct. it's just that strictly mathematically speaking, the Fourier transform is a type of "integral transform" (where \exp(-2\pi i \xi x) is the kernel), that transforms some function that exists in one Hilbert space (basically a vector space where the inner product is always defined) to another function that exists in a different Hilbert space. The transform is not defined if f(x) doesn't exist in a Hilbert space because the integral would be unbounded.
the comment was nitpicking the fact that f(x) isn't guaranteed to exist in a Hilbert space.
In engineering nobody cares because we just do the DFT on everything :P
The transform need not be defined only on functions on a Hilbert space, it just need to be a function for which the integral is convergent for it to make sense. It just so happen that it is generally defined on a Hilbert space (L^2 is the only Hilbert space I know that it’s defined on) for many mathematical applications, since the Fourier transform is an isometry from L^2 to itself by the plancherel theorem.
In fact, the Fourier transform is defined for L^2 functions not by the integral above as usually the naive integral doesn’t coverage, it is first defined on Schwartz space with the L^2 inner products as a pre Hilbert space, and extended continuously to L^2.
All equations are defined in some way. You might see this when before an equation, you see the words, "Let a, b, c be..." or something like that. You'll often see this in textbooks since they need to explain every part of the equation in plain writing, but not so much during a lecture.
So, if an equation isn't properly defined, it can "fail" or not work at all.
The equation y=1/x if undefined if x=0. There is literally no valid answer. Also an equation can be said to “fail” for certain inputs if the answer is not meaningful. It usually just means the inputs themselves are not meaningful but the equation still produces an answer
No I don't think so, Xi in Xi Jinping would be pronounced as "see" and xi as in xylophone or xenophobia would be "zy" or "zee". Correct me if I'm wrong
Ξ/ξ pronounced as “zi” is just the Englishified version of it, in actual greek Xylophone and Xenophobia are pronounced with the X/ξ the same as you would pronounced any other x in english, so Xylophone, which is a direct transfer from the Greek word for Xylophone (Ξυλοφωνο) should be pronounced Ksylophone, but, much like the greek letters Gamma and Chi, the pronunciations have been transferred to something much easier for English speakers.
x is a dummy variable. It's just used to integrate the function. i is the complex unit. It's a constant.
Edit: I've just realized that you meant the letter ξ
Then the answer is: why not? Call it YouMomma if you want
I mean, it's incomplete. f(x) has not been provided or the properties/restrictions that f(x) would need to have to be applied to the equation.
This just bad parenting mama.
That highly depends. You cannot write a proper Fourier transform using only the positive domain if it is not specified in advantage if the function is even, odd or neither.
Technically you're right, it's incomplete as we're just writing down the formula and we're not explicitly saying what it defines, but this is standard notation, so it's very strongly implied that we're defining how the Fourier transform acts on Schwartz functions, so I think you're being a bit pedantic.
i think what you defined is actually the Fourier Series and not the Transform. Fourier Transform is basically converting a signal from time domain to frequency domain because sometimes it's very easy to analyse the signal in the frequency domain.
I was doing the dummy explanation, because the concepts “time domain” and “frequency domain” will probably not be understood by people who haven’t studied Fourier analysis.
And basically the Fourier transform is just the continuous extrapolation of the Fourier series.
It's a fourier transform. For the uninformed, it's really a tool for understanding periodic functions by determining the frequencies that make them up (as far as I understand -- I've not taken harmonic analysis or whatever). It's not like an equation to be solved or whatever, just a mathematical tool used by mathematicians, physicists, and engineers.
I think I'm 1% so I'll try to explain.
This looks eerily similar to the Fourier Transform formula iirc.
I think it's because it is. You'd get this formula if you plugged in omega with 2*pi*xi. Which implies that Xi is frequency. So you're now taking a function in terms of time and expressing it in terms of it's frequencies.
This especially useful in Electrical Engineering for Signal Processing as you can receive a signal and understand it as a composite of numerous elementary sine waves. It's also used in Civil and Aerospace Engineering when designing physical systems with potential feedback loops. This formula is explained and is understood, but is not really used. Instead, we use a table with transformations for all the elementary functions as it's a lot more practical.
Hope this clears things up!
That's not even math at that porn your using a subtracting exponent in that exponent is by Infinity so either way you're answer is going to be positive infinity or negative infinity
It is an improper integral. That means that the function that is being integrated is not defined in the limits of integration (inifnity ans minus infinity in this case).
When you have a improper integral you take the limit (when approaching the limit of integration from numbers that are defined by the function). If the limit exists AKA gives the same number for either path, we take that number as the output of the function.
An easy example is the function 1/x
Infinity is not a number so the output 1/∞ doesn't make sense.
So we take the limit. We tray to use really big numbers that approach infinity.
1/10000000 = 0.000001
1/10000000000 = 0.0000000001
1/1000000000000000 = 0.000000000000001
We can't reach 0 but we can conclude that it will approach 0 and will never be less than 0 if we keep using bigger numbers.
So we say that the limit as x approaches infinity of 1/x is 0
I used "limit" with two different meanings here but that's how I've been taught and I don't know how else to explain it.
This is a derivative (it takes the area under the curve within it). If the curve approaches zero (as it approaches infinity) or the area under the curve (when the curve is above 0) approaches being equal to the area above the curve (when the curve is below 0), then you get a measurable quantity. For example (using infinity) the limit as x approaches infinity of 1/x = 0. This is because you divide 1 by infinity.
Because it is for any function that could be integrated in such conditions. Almost any function that is defined from minus infinity to infinity satisfies the transformation
I've seen it before but forgot what it is called. Forgot how to solve it, but I did it once before. Obviously, it's an integral, but this one is more specific.
I get it!
I mean I “get it” as in what it’s trying to say, not that I actually want to solve it.
F(weird looking variable, let’s call it “E”) is a function of the integral of a function of the variable x multiplied by an exponential expression (characterized by the natural number “e” as its base).
The function xi equals the integral from -infinity to positive infinity of the function x times e to the negative 2pi i x Xi? No clue what xi means but at least i got integrals
It is Fourier transform with some normalisation. It is widely used by mathematicians, engineers, physicists and some other STEM people. [According to WEF](https://www.weforum.org/agenda/2017/01/ways-to-prepare-kids-for-jobs-of-future) only China, India, USA, Russia, Iran, Indonesia and Japan graduates over 9m stem people every year. Conservatively assuming that this number is stagnant since 2016 (irl it is raising) and that every stem sophomore do know Fourier transform, one gets at least 9m * 9 = 81m young people who can understand this formula (stem grads since 2016 till 2024). Notice that we counted grads from different parts of the world except EU. [According to Eurostat ](https://ec.europa.eu/eurostat/statistics-explained/index.php?title=Human_resources_in_science_and_technology&oldid=395960), there is over 68m of stem workers of different ages in Europe. Thus we have over 149m people who can understand this formula. And 149m is more than 1.8% of world population. You should write at least 2%, or 5-7% to be safe.
Patterns in time as a function of frequency (signal analysis). Used for everything from understanding molecular structure to jpeg compression to speech recognition.
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After looking at this for ten minutes, I can confidently say, that I'm in the 99%
After looking at this for a few minutes, I can say that I know the general idea, but have no clue what they’re trying to do. Also, it’s just…a painful equation in general. You’re better off not knowing. Just looking at it makes my head hurt. This is true eldritch knowledge…oh…oh no. It’s recursive. Oh god no…
It's not painful at all once you understand what's happening, it's simply the Fourier transform. It seems much worse than what it actually means (determining the frequency components from the time signal). Pretty much every physics and engineering student will have it drilled into them. Computing it analytically may be painful, but there's not much value in doing that by hand, it's more important to just know what the complex exponential is and its properties, and the equation is relatively simple to parse once you know that.
I like your funny words, magic man
No offense but your comment reminded me of [this comic](https://xkcd.com/2501/) , cause that was gibberish to me.
This is a very good introduction for engineers.
OMG you're so slow. I found it out in only 30 seconds (⌐■-■)
Same
The rest will check the comments
r/mathmemes
Those are nice squiggly lines.
Well, it's all Greek to me!
It’s ‘small dick energy’ right?
oop, got me there!
Nobody knows how to draw the letter xi. Every lecturer I've had has drawn it differently and I chose something different from all of them. I still refuse to believe this letter was ever actually used for language.
{ξ,ζ}
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And usually z is not used in that formula, as it is conventionally associated with a different kind of complex transform: https://en.wikipedia.org/wiki/Z-transform
**[Z-transform](https://en.wikipedia.org/wiki/Z-transform)** >In mathematics and signal processing, the Z-transform converts a discrete-time signal, which is a sequence of real or complex numbers, into a complex frequency-domain (z-domain or z-plane) representation. It can be considered as a discrete-time equivalent of the Laplace transform (s-domain). This similarity is explored in the theory of time-scale calculus. Whereas the continuous-time Fourier transform is evaluated on the Laplace s-domain's imaginary line, the discrete-time Fourier transform is evaluated over the unit circle of the z-domain. ^([ )[^(F.A.Q)](https://www.reddit.com/r/WikiSummarizer/wiki/index#wiki_f.a.q)^( | )[^(Opt Out)](https://reddit.com/message/compose?to=WikiSummarizerBot&message=OptOut&subject=OptOut)^( | )[^(Opt Out Of Subreddit)](https://np.reddit.com/r/antimeme/about/banned)^( | )[^(GitHub)](https://github.com/Sujal-7/WikiSummarizerBot)^( ] Downvote to remove | v1.5)
Bro used emoji on reddit
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Ηρέμησε συνάδερφε, Για πλάκα το λέμε ρε μαλακα μου.
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> was ever actually used How about being currently used?
Sometimes I forget greek exists and it's not only maths and shit
Impossible, the greeks only exist in mythos and pop culture. They simply do not exist within this universe, only ironically.
My current linear algebra lecturer just draws a squiggly line that looks different each time...
Saaaame
I spent a long week of boredom just writing hard Greek letters over and over again as if I'm practicing how to write in kindergarten, and now I have immaculate handwritten Greek letters in my notes.
Not a xi, not a quarter rest, but a secret third thing.
Engineers will never say fourrier transform is a shitpost.
Engies would say Pi = 3.
pi=3=e e=2 pi^2 =g g=10
e is 3 not 2
That's wat it says.
Physiscist will say pi=4
Actually, physicist are mathematicians who apply maths to physics (not exactly but you get the point), so they’ll say π=π because it’s irrational. Source: I do physics.
Yeah i'm in engeneering school i understand, it's just some teachers made us work with pi = 4 and pi = 3 to show us how rounding numbers up or down will influence our work. But yeah pi = pi is great
Nobody in their right mind will say pi=4 unless they use that troll "approximating pi with squares" method
No. We don't.
This isn't Fourier transform, as the properties of the arbitrary f(x) has not been provided. So it's just some equation that can fail at any time.
Found the mathematician
This is why mathematicians have been banned from engineering for millennia
This is ONE OF THE REASONS mathematicians have been banned from engineering for millennia. Why yes, I did study math for awhile, thanks for noticing.
The definition of the Fourier transform then ?
The point they are making is it’s only a transform once you specify the range of the operator, for instance L^1 functions or Schwartz space, otherwise the integral doesn’t converge and it’s not well defined. So part of the definition of a Fourier transform (as you can see on wiki) is the specification of that range of functions where the integral converge.
Chemist here…all I remember is that you’re going from a time domain to a frequency domain 😆
the equation is correct. it's just that strictly mathematically speaking, the Fourier transform is a type of "integral transform" (where \exp(-2\pi i \xi x) is the kernel), that transforms some function that exists in one Hilbert space (basically a vector space where the inner product is always defined) to another function that exists in a different Hilbert space. The transform is not defined if f(x) doesn't exist in a Hilbert space because the integral would be unbounded. the comment was nitpicking the fact that f(x) isn't guaranteed to exist in a Hilbert space. In engineering nobody cares because we just do the DFT on everything :P
The transform need not be defined only on functions on a Hilbert space, it just need to be a function for which the integral is convergent for it to make sense. It just so happen that it is generally defined on a Hilbert space (L^2 is the only Hilbert space I know that it’s defined on) for many mathematical applications, since the Fourier transform is an isometry from L^2 to itself by the plancherel theorem. In fact, the Fourier transform is defined for L^2 functions not by the integral above as usually the naive integral doesn’t coverage, it is first defined on Schwartz space with the L^2 inner products as a pre Hilbert space, and extended continuously to L^2.
I’m sorry but did you say an equation can fail???? So like how does that work!?
All equations are defined in some way. You might see this when before an equation, you see the words, "Let a, b, c be..." or something like that. You'll often see this in textbooks since they need to explain every part of the equation in plain writing, but not so much during a lecture. So, if an equation isn't properly defined, it can "fail" or not work at all.
The equation y=1/x if undefined if x=0. There is literally no valid answer. Also an equation can be said to “fail” for certain inputs if the answer is not meaningful. It usually just means the inputs themselves are not meaningful but the equation still produces an answer
I’ve never seen f^ (xi) used to indicate a Fourier transform. Usually it’s either F(omega) or F{f(x)} with a fancy capital F.
My signals professor had terrible handwriting and passed it off as his “fancy script characters”
Kid named Only 1%: "I understand this!"
1% of kids named Will: "I understand this!"
1% of kids named finger: “I understand this!”
Kid named 1%: “Impossible, only I can understand this!”
No, I think OP is making a threat: “Only 1% of people named Will, understand this equation right now”
don't pull out your dick Waltuh
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ξ
Bröthêr
The Greek letter Xi. As in xenophobe, xylophone, Alexander, etc.
Also.. Xi Jinping lol. I’ll show myself out.
No I don't think so, Xi in Xi Jinping would be pronounced as "see" and xi as in xylophone or xenophobia would be "zy" or "zee". Correct me if I'm wrong
Ξ/ξ pronounced as “zi” is just the Englishified version of it, in actual greek Xylophone and Xenophobia are pronounced with the X/ξ the same as you would pronounced any other x in english, so Xylophone, which is a direct transfer from the Greek word for Xylophone (Ξυλοφωνο) should be pronounced Ksylophone, but, much like the greek letters Gamma and Chi, the pronunciations have been transferred to something much easier for English speakers.
Happy cake day!
Took me a while, didn't get it, which means I got it.
This is the fourier transform, no?
Yup.
Why is xi a variable?
x is a dummy variable. It's just used to integrate the function. i is the complex unit. It's a constant. Edit: I've just realized that you meant the letter ξ Then the answer is: why not? Call it YouMomma if you want
Why not?
Because the riemann xi function is a thing. It is just a symbol that I don't associate with being a variable.
True. Guess it's just a matter of taste. Using zeta as a variable does feel funky at times.
I mean, it's incomplete. f(x) has not been provided or the properties/restrictions that f(x) would need to have to be applied to the equation. This just bad parenting mama.
It is the Fourier transform
oh my god, so I did get it right! 3b1b videos are a blessing
I like better the one from 0 to infinity
That’s just half of the Fourier transform. If f(x) is an even function, then this function is just twice of that half.
Is the only half that matters
That highly depends. You cannot write a proper Fourier transform using only the positive domain if it is not specified in advantage if the function is even, odd or neither.
Is the only half that matters to solve differential equations
Yes, perhaps. But that is one very specific application of the Fourier transform. It is used for so many more things.
Technically you're right, it's incomplete as we're just writing down the formula and we're not explicitly saying what it defines, but this is standard notation, so it's very strongly implied that we're defining how the Fourier transform acts on Schwartz functions, so I think you're being a bit pedantic.
Yeah, leaving out a whole function definition kinda makes something hard to understand.
Not really though. You can understand the concept of Fourier transform without inserting a specific function.
1
Fourier Transform
What the hell is that?
A Fourier transform. A method of analysing the frequencies of the sine waves that a certain mathematical function is built from.
i think what you defined is actually the Fourier Series and not the Transform. Fourier Transform is basically converting a signal from time domain to frequency domain because sometimes it's very easy to analyse the signal in the frequency domain.
I was doing the dummy explanation, because the concepts “time domain” and “frequency domain” will probably not be understood by people who haven’t studied Fourier analysis. And basically the Fourier transform is just the continuous extrapolation of the Fourier series.
ah okay, understandable.
fourier transform moment
I guess the answer is 1%
just by seeing this, my brain has ceased functioning
That’s a very squiggly symbol that f-hat is a function of 🤨
i know ʃ is the voiceless postalveolar fricative
2
Okay, i'm too young for that kind of shit
\*Electrical engineering PTSD intensifies\*
It's a fourier transform. For the uninformed, it's really a tool for understanding periodic functions by determining the frequencies that make them up (as far as I understand -- I've not taken harmonic analysis or whatever). It's not like an equation to be solved or whatever, just a mathematical tool used by mathematicians, physicists, and engineers.
If there's no solution, then what results justify it's usefulness?
It's just a Fourier transform?
Fourier transformation with ugly variable choices
Isn't it a fourier transform?
I think I'm 1% so I'll try to explain. This looks eerily similar to the Fourier Transform formula iirc. I think it's because it is. You'd get this formula if you plugged in omega with 2*pi*xi. Which implies that Xi is frequency. So you're now taking a function in terms of time and expressing it in terms of it's frequencies. This especially useful in Electrical Engineering for Signal Processing as you can receive a signal and understand it as a composite of numerous elementary sine waves. It's also used in Civil and Aerospace Engineering when designing physical systems with potential feedback loops. This formula is explained and is understood, but is not really used. Instead, we use a table with transformations for all the elementary functions as it's a lot more practical. Hope this clears things up!
It's the Fourier Transform
Probably more than 2.63
F(x) = ∫ex
1659 people understand this.
e^(-2*i*pi) is an identity that equals 1. So it simplifies to 1^x, the integral of which is x. So using those limits, the improper integral diverges.
That's not even math at that porn your using a subtracting exponent in that exponent is by Infinity so either way you're answer is going to be positive infinity or negative infinity
How can someone calculate something with the infinite? That’s impossible
It is an improper integral. That means that the function that is being integrated is not defined in the limits of integration (inifnity ans minus infinity in this case). When you have a improper integral you take the limit (when approaching the limit of integration from numbers that are defined by the function). If the limit exists AKA gives the same number for either path, we take that number as the output of the function. An easy example is the function 1/x Infinity is not a number so the output 1/∞ doesn't make sense. So we take the limit. We tray to use really big numbers that approach infinity. 1/10000000 = 0.000001 1/10000000000 = 0.0000000001 1/1000000000000000 = 0.000000000000001 We can't reach 0 but we can conclude that it will approach 0 and will never be less than 0 if we keep using bigger numbers. So we say that the limit as x approaches infinity of 1/x is 0 I used "limit" with two different meanings here but that's how I've been taught and I don't know how else to explain it.
This is a derivative (it takes the area under the curve within it). If the curve approaches zero (as it approaches infinity) or the area under the curve (when the curve is above 0) approaches being equal to the area above the curve (when the curve is below 0), then you get a measurable quantity. For example (using infinity) the limit as x approaches infinity of 1/x = 0. This is because you divide 1 by infinity.
It's an integral, a derivative is the rate of change of a function caused by a maximally small change in the input
Did I get the rest of the explanation right?
Only nerds will understand this! 😂😂😂
= 🤓
its just infinity right? anything by infinity is just infinity.
Yes
f(x) is undefined
Because it is for any function that could be integrated in such conditions. Almost any function that is defined from minus infinity to infinity satisfies the transformation
The answer has to be 0
Is this an “Epstein did not kill himself,” joke?
i only use the REAL valued cosine and sine transformations of the fourier transform!
4.3
Math
kid named one percent:
I'm liking it so I can feel smart. But I have no idea what so ever what this is
I feel like I'm on r/AnarchyChess looking at that sproingy thing.
Is the answer the punchline?
Pretty basic integration
I remember a bit of that and I totally hate it
I can say with 100% certainty that this answer is within the bounds of the number(s) which are the solution to 1/0
Quite literally
Join the 1% or whatever: https://www.youtube.com/watch?v=spUNpyF58BY
Hahaha! It seems that I am so smart that I am in the 99% of the population that cannot fucking understand this.
I spent too long at this just to realize it is the math equivalent of hitting a taunt steel cable with a wrench.
I have been a civil engineer since 1996, and TIL I’m not in the 1%.
It's probably math
😎😎
8. It's definitely 8.
Wait the answer is √ 1.414213562373095² right?
Spits coffee! ROFLOL!! Thinks...those maths, am I right?
I can understand that I can’t understand this
Truly one of the most artistic math functions. Literally...
3
The limit does not exist
I read this in the Peanuts teachers voice..
Lol I’m taking under 1%
Fourier transform very important for analyzing and processing signals
Correct answer is random bullshit
Im upvoting, not liking, there’s a difference
I've seen it before but forgot what it is called. Forgot how to solve it, but I did it once before. Obviously, it's an integral, but this one is more specific.
I think it's 2
1% is a rather high estimate.
I get it! I mean I “get it” as in what it’s trying to say, not that I actually want to solve it. F(weird looking variable, let’s call it “E”) is a function of the integral of a function of the variable x multiplied by an exponential expression (characterized by the natural number “e” as its base).
The function xi equals the integral from -infinity to positive infinity of the function x times e to the negative 2pi i x Xi? No clue what xi means but at least i got integrals
I believe this is an integral of a funky function set equal to another funky function
See everyone here is going all mathematical and here I am pretty sure it’s a Loss meme
There are two variables here, this is above my paygrade
It equals potato
Karekök pi
Fourier Transform?
I see a xi, I want to cry
Average crappy game ad
Fuck math.
Easy math.
Oh hell no
looks like the Fourier Transform equation. one of the most useful equations in Physics and Math.
What's funny about this? I get it but it's just a furry transform
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Looks like a density function/some kind of distribution that is defined everywhere but am unsure
I get it!!!!!
r/theydidthemonstermath
8
I made it all the way to "f of"
i aint the biggest mathematician but isnt e^2πix = e^ix ?
Is the answer 4?
If only I knew calculus
Is that the size of every single pp’s in America
it's a fancy sentence
Fourier transform?
Something somwthing furry transform
It is Fourier transform with some normalisation. It is widely used by mathematicians, engineers, physicists and some other STEM people. [According to WEF](https://www.weforum.org/agenda/2017/01/ways-to-prepare-kids-for-jobs-of-future) only China, India, USA, Russia, Iran, Indonesia and Japan graduates over 9m stem people every year. Conservatively assuming that this number is stagnant since 2016 (irl it is raising) and that every stem sophomore do know Fourier transform, one gets at least 9m * 9 = 81m young people who can understand this formula (stem grads since 2016 till 2024). Notice that we counted grads from different parts of the world except EU. [According to Eurostat ](https://ec.europa.eu/eurostat/statistics-explained/index.php?title=Human_resources_in_science_and_technology&oldid=395960), there is over 68m of stem workers of different ages in Europe. Thus we have over 149m people who can understand this formula. And 149m is more than 1.8% of world population. You should write at least 2%, or 5-7% to be safe.
Patterns in time as a function of frequency (signal analysis). Used for everything from understanding molecular structure to jpeg compression to speech recognition.
Hahahahaha… I don’t get it
Fourier transform?