What Is the Fourier Transform?
quantamagazine.org
What Is the Fourier Transform?
1–10 of 214 posts
Re: What Is the Fourier Transform?
#2Always blew my mind that every signal can be recreated simply by adding different sine waves together.
Re: What Is the Fourier Transform?
#3Always blew my mind that every signal can be recreated simply by adding different sine waves together.
Taking the concept to a 2d path: https://www.myfourierepicycles.com
And, with your own drawing: https://gofigure.impara.ai
Re: What Is the Fourier Transform?
#4[flagged]
Re: What Is the Fourier Transform?
#5Always blew my mind that every signal can be recreated simply by adding different sine waves together.
Only if it is band-limited.
Re: What Is the Fourier Transform?
#6[flagged]
This kind of statement is too vague to be useful. I even know all the words in there and I still don't know what you mean.
Re: What Is the Fourier Transform?
#7Always blew my mind that every signal can be recreated simply by adding different sine waves together.
Back in my uni days I did not get why that works. Why are sine waves special?
Turns out... they are not! You can do the same thing using a different set of functions, like Legendre polynomials, or wavelets.
Re: What Is the Fourier Transform?
#8See also its windowed version, https://en.wikipedia.org/wiki/Short-time_Fourier_transform
Re: What Is the Fourier Transform?
#9Re: What Is the Fourier Transform?
#10[flagged]
Hmm I always viewed it as sum over orthogonal bases. Sine/Cosine is choice, while there can be many other bases, like Legendre polynomials. Can you explain more how FT is linked to 'a sum over equivalence classes'?