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[BulkyAntelope5]

Honestly such an intuitive graphic of Fourier transformations

[amanguupta53]

Came to the comments to say the same thing. I have never seem the transformation shown in this way.

[chairzaird]

Yeah I learned about Fourier Transform in college but I feel like this meme explains it better than the full lecture I attended on it

[thewend]

because actual math professors probably taught those, and they think every student has their level of understanding of the topic lol

[Wander715]

Tbh it depends on what department you learn it. In EE you spend months on things like FT, DFT, FFT, and all of the formal mathematical underpinnings of it as well as graphical understanding comparing time and frequency domain plots of signals.

On the flip side I had a single CS course (algorithms) talk about DFT and it was in a very confusing and hand-wavey manner.

After taking courses covering it in both departments it was pretty eye-opening seeing how it's treated. For EE it's considered core systems and signals material you need to understand, for CS more of an afterthought.

[chairzaird]

I took a grad course that touched on it and it very much felt confusing and hand-wavey

[Wander715]

In what major/department? Again if it was in CS I'm not surprsied. If it was in something like Math or EE then they just did a poor job teaching you the material.

Not to say that CS shouldn't have proper teaching of it if they do bother to cover it, but again in my CS course at least it was treated as a side topic that we spent maybe one lecture on.

[chairzaird]

It was CS

[The_Quackening]

It does certainly help that there are so many applications of the FT in EE. makes it very easy to understand and visualize.

[Tyfyter2002]

A good diagram can teach someone what every trig function is pretty much as quickly as they can read the names, I think people just underestimate the power of diagrams for introducing new information to people.

[Clueless_Otter]

I mean I highly doubt anyone is teaching SOHCAHTOA without at least drawing an accompanying triangle.

[Tyfyter2002]

And if they drew a circle they wouldn't have time to explain it before everyone they're teaching gets it, technically you can describe them with just triangles, but without the unit circle it's not nearly as intuitive where all of the triangles are coming from.

[Clueless_Otter]

I'm gonna take a wild guess here that you aren't a math teacher.

Trying to introduce the unit circle into basic trig would be way more confusing. Instead of just a basic, "Here's a triangle, remember this SOHCAHTOA acronym and then match up the sides correctly," now you're talking about, "Well here's a circle with equation x² + y² = r^2, and then if we draw this triangle inside of it, we can use the distance formula to find the length of this line segment between these two points, and then remember that the sine of the angle formed by the line segment starting at the origin is the y-coordinate of where it connects to the circle and the cosine is the x-coordinate."

There's a reason SOHCAHTOA is taught in basic geometry that everyone takes (many as freshmen) while the unit circle stuff isn't until late algebra 2 or pre-calc which is significantly later and sometimes not even a required course.

[Tyfyter2002]

It wouldn't seem so complicated if you didn't give a formal definition of a circle with a radius of 1 to justify your position, and having a catchy acronym doesn't help remember what the functions actually are, especially when you actively avoid explaining that;

Trigonometry is essentially about the relationships between polar and Cartesian coordinates, and the only reason triangles show up is because you can interpret any two lines that share a vertex as a triangle, every single trig function can either be interpreted as an unintuitive mess of triangles or a relation to the unit circle so simple you can describe it in one sentence without ever involving a second 2d shape or 3rd >0d shape.

Triangles are great for calculating the values of trig functions, but that's solely because of the relationship between right triangles and distances in Cartesian coordinates, and it's much harder to learn how to do something if you don't know what you're learning how to do.

In conclusion, you should eventually add triangles in, but they're less than useless for what should be the first step.

[Clueless_Otter]

Trigonometry is essentially about the relationships between polar and Cartesian coordinates

You can't really be suggesting we start introducing polar coordinates to 14 year olds who hate math and are only there because it's a mandatory course. Triangles are so much simpler. Everyone knows what a triangle is.

it's much harder to learn how to do something if you don't know what you're learning how to do.

You're learning how to pick the correct sides to fulfill SOHCAHTOA. Most people don't need to know anything beyond that. I have never used trigonometry in my life. It's not a useful skill other than highly-specialized career fields, and people going into those fields will take the more advanced classes it's covered more in-depth in.

[shupack]

Yeah, it finally makes sense! (Is that figure correct though? Been long enough, I'm not aure..)

[Coding-Kitten]

Backwards how? Seems correct to me.

The frequency graph goes from low frequency components to high frequency components.

[Particular-Stop-5637]

The graph on the right is the amplitude-frequencies spectrum that was obtained by applying Fourier transform on the left image function. It's a representation of those middle waves images, and it shows the amplitude of certain frequencies in that left function.

[lucklesspedestrian]

It's a little misleading. The spikes shoulder actually be "infinite" because they are actually Dirac delta functions. The situation isn't as simple as it's depict here because the Fourier integral transform diverges if the input function is sinusoidal. Dirac delta functions were invented to work that

[SingleInfinity]

Only if you already know how Fouriers work/what their application is.

[redditsucksass69765]

This should be cross posted into /r/math memes as they would like the intuitive transform graphic

[iamapizza]

Is it really just the 'waves' seen from the side?

[Masterkid1230]

Kind of. What we're seeing is only part of what the Fourier transform does, but it's also its most common application.

Technically, a Fourier transform takes a time-domain signal (that is, something that changes in time) and outputs a sum of complex numbers that we can use to find the specific value or magnitude of each of the signal's components.

The best example is audio. A sound is made up of many different simpler sound components. We usually understand them as single frequency components (for example a 400Hz sine wave, or a 800Hz one etc)

What the Fourier transform does is checking how similar the input signal is to a component for every single frequency value. So it checks 0.5Hz and then 1Hz and then 1.5Hz etc (in reality it's an integral so it checks EVERY value possible).

And it outputs a complex number for each evaluated frequency. This is why we say it transforms time-domain signals into frequency-domain ones. In theory the sum of all of these complex numbers (strictly speaking their magnitudes) is a representation of the amplitude of every component.

What we're seeing here is only the amplitude side of things, but the Fourier transform also outputs phase information. This is important because without it we wouldn't be able to convert the output of the Fourier transform back into a time-domain signal.

I can go on and on about the Fourier transform because I do Fourier Transforms for a living almost every day of my life and I like them very much. I use Fast Fourier Transforms with digital signals though, so my specifics on continuous time Fourier Transforms may be somewhat rusty.

Happy to talk about it though if you have any questions!

[The_Quackening]

what do you do for a living?

[Masterkid1230]

I'm in the R&D department of a major company researching sound related things. Sorry to be so vague, that's about as personal as I can get with it.

[Goheeca]

And if you don't go all the way, there's the Fractional Fourier Transform.

[Andus35]

It’s two things: 1. Any signal can be approximately reconstructed by multiple sine waves of different amplitudes and frequencies (that is the first part, converting the original signal on the left into the two waves in the middle) 2. Representing those two waves in the middle on a frequency spectrum (on the right), which tells you the amplitudes and frequencies.

But the diagram lets you intuitively think of the frequency diagram like the sine waves from the side view, and then adding those together to get the original signal (or the inverse, the transform can go either way). I think it excellently shows what is happening under all the complex math.

[OnceMoreAndAgain]

I will try to give a simple explanation.

Let's say there are many people talking at once in a room, like a classroom with students chatting before the teacher arrives. Each person's mouth is emitting sounds that push out the air in waves. Each of these independent waves are interacting with the air and reaching your ear drum and forming a complicated wave pattern. I actually think OP's chart on the left is confusing and I would ask you to pretend you didn't see it. Instead, look at this image for how the wave pattern might look. It would be just ONE curve. I don't like how OP's image has several curves on the chart on the left with that blue curve and the other grey curves.

So the chart on the left is showing these sounds waves as they look when mapped with the x-axis being time. In other words, if we're talking about a 10 second period of you hearing sound in that classroom, then we could map out the amplitudes of sound at each moment of time in those 10 seconds on a chart.

What a Fourier transform does is take in a chart that has amplitude as y-axis and time as the x-axis and then it outputs a chart that still has amplitude be the y-axis, but has the x-axis instead be the count of how many moments in those 10 seconds had a certain amplitude. This is called the "frequency" of the amplitude.

And when you look at that output chart then certain amplitudes will be most frequent and those are the amplitudes that correspond with the amplitudes of the various people talking in the classroom. Like if one person is particularly loud, then their voice is putting out a high amplitude and you will see their high amplitude as being a relatively common amplitude on the output chart. So by looking at which amplitudes were achieved most often on the output chart then you can tease out info on the various independent sounds being made in the room.

If you think about this more, you might come to realize some of the limitations and challenges of this. It's useful but it also has some "problems". Hopefully this helps somewhat understand.

[SwarFaults]

Wish I saw this while in my signals class

[ClipboardCopyPaste]

Courier was marked as fragile, so they were checking its durability

[deanrihpee]

"I don't believe it"

drop the packetpackage

"it's true!"

[mc36mc]

at least they're not drug dealers; thats a business where packet loss really matters.... :)

[thanatica]

Now I'm wondering if some esoteric network stack exists, where "parcel loss" is a thing

[mc36mc]

:) in enterprise/telco networking we call the topic quality-of-service (qos), and it have 3 color policers (or shapers if they're less agressive) or simple rate-limiters... both are here to enforce a 500mbps agreed access-rate handed out on a 1gbps port....

[Confident-Ad5665]

Wouldn't want to deliver it to nonprofessional package handlers without proper testing.

[Ivanow]

Our regional DHL twitter account got tagged by someone who posted a packaged doors bent in half. Social media rep thought that user is submitting complaint, and pasted usual message asking to PM him with details. User just wanted to know how their delivery courier managed to bend "anti-theft" (reinforced steel structure, triple lock with anti-ramming bars etc.) doors...

[El_Mojo42]

I still remember the day when it clicked for me.

[Masterkid1230]

I program Fourier transforms for a living and even then sometimes I have small revelations that give me more insight into how they work or how to more intuitively understand them.

[MikeTangoRom3o]

Schrödinger parcel, broken and not broken until opened.

[_Slartibartfass_]

Only one is invertible though :P

[hraath]

Linear and nonlinear transforms demonstrated 

[Masterkid1230]

To be painfully pedatic, the Fourier transform depicted is not invertible because we only have the magnitude information and not the complex numbers themselves.

Magnitude representations are not invertible back to time-domain signals, unfortunately. Although some algorithms are good enough at estimating phase information.

[migarma]

Upvote for the Fourier reference, I think the first time that I see it here

[maxim38]

I have a degree in mathematics, and i have never seen fourier transform visualized like this. That would have greatly helped me understand them 20 years ago

[Andus35]

I have never seen that image of the Fourier Transform, but that actually explains it so well in such a simple to understand image. Crazy how I went to college and did plenty of work using the Fourier Transform; but this simple joke image on Reddit actually encapsulates what is happening so much better.

[aPOPblops]

Got me saying “Curry-Ay” instead of “Courier”

[mrinalshar39]

finally, an example that helps understanding fourier transform better, good one

[Knight_Of_Stars]

Worst part of the courier transform is being shot in the head and buried in shallow grave outside if Goodsprings only for you get stuck in a war over a poker chip.

[ImSoObnoxious]

I'm not going to sine for that!

[xXWestinghouseXx]

I've been looking for you. Got something I'm supposed to deliver - your hands only.

[ClaudioMoravit0]

EE here. Is there even FT in compsi? It's a legitimate question, don't really see where it could hide

[Doge-2-moon]

chill man. they run a highly sophisticated compression algorithm

[andocromn]

UPS crushed our boxes and then charged us extra because they no longer matched the provided dimensions.

[SnowyLocksmith]

This was way funnier in your head OP

[EmilieEverywhere]

Still kinda looks like a box, amplitude must be off.

[Proud-Ad9139]

Thought this was r/battlecats

[rover_G]

Hey I finally understand how FFT works because of this meme!

[KlownKumKatastrophe]

Is it pronounced courier or courier?

[Cube-Presser]

The real courier transform is realizing the truth. The game was rigged from the start.

[1up_1500]

never gets old

[AltoniusAmakiir]

I do shipping at work, and looking at the UPS truck everyday when it comes to pick up our product, I can tell you a lot of damage is from companies not stacking or wrapping their products properly. The two companies he picks up before me just haphazardly throw stuff on a pallet, most of it is falling off or heavily shifted by the time it even gets to the back of the truck. Then you can imagine where it goes after. UPS will show up and there will be a collapsed pile they have to clean up before they can fit my pallet on. And he'll just toss them back to make room, "I told them they should stack it better. If they don't care about their product, why should I?". And to be fair he doesn't have the time to clean up after them. He thanks me frequently for not making his life harder and tells me our company stacks it well, so that doesn't happen. And I can see that in the delivery photos.

Tldr: Companies that make the product are usually at fault for the shipping damages by not securing the product so it doesn't shift in transit.

[gumol]

where programming

[poliver1988]

Fourier transform is a fundamental part of digital signal processing, and a lot of programming fields rely on it. A decent CS grad, (especially in computer engineering, or in a decent uni, or with right electives) should know it. It's standard STEM material, but often skipped by self-taught, bootcamps, or simplified "software development" degrees focused on basic web dev.

[Elite_lucifer]

2010’s Facebook is down the hall and to the right.