For an additional video exposition, I also like Eugene Khutoryansky's "Fourier Transform, Fourier Series, and frequency spectrum"

https://www.youtube.com/watch?v=r18Gi8lSkfM

In particular, the visualization of the addition of sine waves of different frequencies in three dimensions is pretty spectacular. It's similar to Mathologer's "Epicycles, complex Fourier series and Homer Simpson's orbit":

https://www.youtube.com/watch?v=qS4H6PEcCCA