An Interactive Introduction to Fourier Transforms
1–10 of 23 posts
Re: An Interactive Introduction to Fourier Transforms
#2Wow. This is by far, hands down, the best way I have ever seen this explained. Just excellently done.
Re: An Interactive Introduction to Fourier Transforms
#3Wow. This is by far, hands down, the best way I have ever seen this explained. Just excellently done.
Exactly my thoughts also. Thank you Jez!
Re: An Interactive Introduction to Fourier Transforms
#4Very impressive end enlightening indeed.
SmarterEveryDay published a video on this topic few weeks back: https://www.youtube.com/watch?v=ds0cmAV-Yek
Re: An Interactive Introduction to Fourier Transforms
#5In the animation at the top, should use a different color for the circles vs. the hand/pen.
Re: An Interactive Introduction to Fourier Transforms
#6Beautiful! How long did it take to make this blog post?
Re: An Interactive Introduction to Fourier Transforms
#7Epic ...thanks
Re: An Interactive Introduction to Fourier Transforms
#8At the time of writing the Gibbs phenomenon -- the overshoot occurring at discontinuities of a square wave, which does not go away no matter how many harmonics are included (see https://en.wikipedia.org/wiki/Gibbs_phenomenon) -- is not correctly represented in these visualisations, implying that important aspects of the underlying maths are obscured. In my opinion this limits the didactic value of an otherwise impressive presentation.
Re: An Interactive Introduction to Fourier Transforms
#9Slightly unrelated, here's a beautiful mathematical approach to the discrete fourier transform with evaluating a polynomial at the nth root of unity in the complex numbers:
https://ocw.mit.edu/courses/electrical-engineering-and-compu...
Re: An Interactive Introduction to Fourier Transforms
#10At the time of writing the Gibbs phenomenon -- the overshoot occurring at discontinuities of a square wave, which does not go away no matter how many harmonics are included (see https://en.wikipedia.org/wiki/Gibbs_phenomenon ) -- is not correctly represented in these visualisations, implying that important aspects of the underlying maths are obscured. In my opinion this limits the didactic value of an otherwise impre…
Yes, apologies I made some approximates in the article!
Interestingly if you're talking about discrete time fourier transforms (which is what we usually deal with in computers with jpegs, mp3s, etc), then you can perfectly represent a signal with say, 1024 samples using exactly 1024 sine waves without worrying about that effect. It's only in the continuous time variant that you have to worry about things like the Gibbs phenomenon (which you do run into once you start translating to real world output)