[…] images are captured from the interactive tool created by Lucas Vieira posted at the bottom of the betterexplained.com article on the Fourier Transform which you can also play around with the recreate the images […]
Hi, thanks for this, it helps a lot. But there is a peculiarity:
“A 1Hz cycle goes 1 revolution in the entire 4 seconds, so a 1-second delay is a quarter-turn. Phase shift it 90 degrees backwards (-90) and it gets to phase=0, the max value, at t=1”
Surely a 0.25Hz cycle goes one revolution in 4 seconds?
@gparley: Thanks, you are correct. I was very loose with my terminology, to avoid the need for decimals.
If a signal had 4 data points (a b c d), I wanted to imagine scaling it up so it took 4 seconds of time to complete. A cycle that would have complete 1/4 of the entire signal each step (.25Hz) could be seen as a “1Hz” signal that went through a data point per second (a, b, c, d).
Similarly, something which completed half the cycle each step (.50) would be a “2Hz” signal which ran through 2 positions per second (a, c, a, c). This is a mental conversion I was running in my head, and I need to clarify this part, thanks!
[…] The scientists next determine crystal size by carrying out a Fourier analysis of the intensity of the signals around spots. A Fourier analysis essentially involves breaking down complex signals into a combination of simple waves to better understand the signals — kind of like taking a meal and figuring out its ingredients. […]
you misspelled “intution”
Thanks, just fixed up.
[…] Cat: Untuk lebih mudah memahani secara visual yang dimaksud dengan bidang imajiner dan real dari gelombang periodik, bisa lihat beberapa animasi gelombang periodik di tautan ini!! […]
Suddenly I discovered the meaning of your site
to make money isnt it?
there you go
you do give some insights Im’ not saying the opposite
but alot of it is hogwash you can find it in many other books
but for pure robots as you say its useful it dazzles
maybe you are the Conway of explanations
@aristogeit: I guarantee you, there’s more effective ways to make money online than through a math blog :). My goal is to help people grok the ideas I struggled with.
@aristogeit: go read those books why to visit this blog and help him make more money if you think that way. Don’t waste your precious time in commenting here. Next time we would take permission from you whether to write blog or not.
Hi,
I just made a 2D fft filtering tool on my website, you can mask off regions of the spectrum as a filter and see the effects by performing an iFFT on the spectrum
http://www.ejectamenta.com/Imaging-Experiments/fourierimagefiltering.html
Thank You.
From what i have seen so far(not too much) this is the best possible way to explain “Fourier transform”. And i must say you did the best.
Thank you again to explain it so clearly.
Hi
Trying to understand your animation - the first one (http://treeblurb.com/dev_math/sin_canv00.html)
On r.h.s. you have a cosine wave which is 1 period long and goes from 1 to -1. And I assume on the l.h.s. you are plotting the values from it on the circle. But how do you get the circle. If you just have a cosine wave, you will oscillate along the x-axis. Don’t you need the sum of cosine+sine to go into a circle ?
Thanks
Asif
Hi Asif, actually that’s not my animation, but the one that inspired my own.
The plot is actually of the height on the circle as we traverse it at a constant speed, so it’s a sine wave. Sine and cosine can be defined on the unit circle, see http://betterexplained.com/articles/intuitive-trigonometry for more. Hope that helps!
A very good explanation, but I wonder if it might be a bit too oversimplified in places? Simplification is good but i think calling them position (0 1 2 3) and then recycling arabic numerals for many other purposes just gets confusing after a while.
Great explanation!
Just a smaalll request…it would be really helpful if you can do a blog on different distributions…poisson, exponential, etc…intution to these would be great.
Hi Shweta, glad you liked it. Thanks for the suggestion – I’d like to do more on probability down the road.
[…] I ended up at Better Explained, which has a page specifically on the Fourier transform explaining all that good stuff up there – about Euler’s formula, about a way to think […]