43816237610 http://1ucasvb.tumblr.com/post/43816237610/the-fourier-transform-takes-an-input-function-f 626 The Fourier transform takes an input function f...

The Fourier transform takes an input function f (in red) in the “time domain" and converts it into a new function f-hat (in blue) in the “frequency domain”.

In other words, the original function can be thought of as being “amplitude given time”, and the Fourier transform of the function is “amplitude given frequency”.

Shown here, a simple 6-component approximation of the square wave is decomposed (exactly, for simplicity) into 6 sine waves. These component frequencies show as very sharp peaks in the frequency domain of the function, shown as the blue graph. In practice, these peaks are never that sharp. That would require infinite precision.

I’m not too happy with this one yet. It’s a bit of a mixture of Fourier series and Fourier transform. The animation could also be a bit smoother in some steps. I may tweak it later.

The Fourier transform takes an input function f (in red) in the “time domain" and converts it into a new function f-hat (in blue) in the “frequency domain”.

In other words, the original function can be thought of as being “amplitude given time”, and the Fourier transform of the function is “amplitude given frequency”.

Shown here, a simple 6-component approximation of the square wave is decomposed (exactly, for simplicity) into 6 sine waves. These component frequencies show as very sharp peaks in the frequency domain of the function, shown as the blue graph. In practice, these peaks are never that sharp. That would require infinite precision.

I’m not too happy with this one yet. It’s a bit of a mixture of Fourier series and Fourier transform. The animation could also be a bit smoother in some steps. I may tweak it later.

 
  1. ohayouplanet reblogged this from 1ucasvb
  2. mathew reblogged this from 1ucasvb
  3. hiromalo reblogged this from 1ucasvb
  4. claireever reblogged this from 1ucasvb
  5. hannahkinskywalker reblogged this from deadheadkid92
  6. deadheadkid92 reblogged this from 1ucasvb
  7. jamyriare reblogged this from 1ucasvb
  8. rajyon24 reblogged this from visualizingmath
  9. laviesupernova reblogged this from 1ucasvb
  10. just-cosmic-dust reblogged this from 1ucasvb and added:
    is there a fandom for fourier transforms
  11. solar--gambling reblogged this from visualizingmath
  12. chillycamille reblogged this from mylifeisborromean and added:
    the graphics are just too cool
  13. lobotomyp0p reblogged this from mylifeisborromean
  14. mylifeisborromean reblogged this from visualizingmath
  15. renew-world reblogged this from visualizingmath
  16. uberscientist reblogged this from visualizingmath
  17. romames-eunt-domus reblogged this from 1ucasvb and added:
    Fourier transform concept
  18. bwansen reblogged this from elfboi
  19. elfboi reblogged this from explodingbat
  20. noonemeansme reblogged this from visualizingmath
  21. sampsoncornelius reblogged this from been-a-long-time-cosine
  22. been-a-long-time-cosine reblogged this from visualizingmath
  23. sweetmarie reblogged this from visualizingmath
  24. gokgunce reblogged this from visualizingmath and added:
    Bir animasyon, bin denklem ve açıklamaya bedel..