Скачать или смотреть This is why math is POWERFUL - APPLYING Fourier Transform | Fourier Transform Ep. 3

In this video, we will learn how to apply the Fourier Transform to a real-world situation, like a musical instrument playing a chord. In such a situation, we don’t know the precise definition of the function we are transforming; we only know its value at each point in time, so we cannot simply plug it into the formula. However, by using the magic of the Fourier Transform and understanding a simple intuition for why the integral changes when it does, we can still transform the function. At the end, we will see all of the formulas and concepts that we learned come together in all of their glory! Apart from being wonderfully intuitive and fascinating, the Fourier Transform is immensely applicable in so many different fields, from harmonic analysis and physics to sound design and music.

Here are the links to the previous two videos:
Fourier Series
   • The FASCINATING Fourier Series | Fourier T...  
Fourier Transform (intro)
   • It’s ESSENTIAL that you learn about the Co...  

Also, here is a link to a video from another channel that explains the intuition behind Fourier Transform really well:
   • The intuition behind Fourier and Laplace t...  
3Blue1Brown provides a different but fascinating take on Fourier Transform:
   • But what is the Fourier Transform?  A visu...  

I mentioned the DFT (Discrete Fourier Transform) and the FFT (Fast Fourier Transform). I may release a video on them in the future. For now, though, here are some great links for research:
https://www.robots.ox.ac.uk/~sjrob/Te...
https://web.mit.edu/~gari/teaching/6....
https://people.eecs.ku.edu/~perrins/c...
   • The Fast Fourier Transform (FFT): Most Ing...  
   • The Fast Fourier Transform (FFT)  

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