An interactive guide to Fourier series (2022)
injuly.in
injuly.in
I've improved my writing over time, so reading an older post makes it feel dated. I'll try to post more rigorous technical articles this year.
If you are interested in interactive explorations of the fourier transform you might also like this visualization I built [1], featuring the not so well known fractional fourier transform.
Wouldn't this effectively make frequency 0?
Later on for the drawings you pick period T to be equal to 1, thus frequency to be 2*pi. This does make more sense both practically and mathematically too.
P.S. A small nit, a typo "f_t and y_t" should rather be "f_x and f_y". Very fun read, thanks!
Yes! Letting the period length approach infinity, would make the lowest frequency (omega_0, also delta each other frequencies) approach 0, effectively turning the discrete sum of the fourier series into an integral, turning the fourier series into the continous fourier transform.
Yes, if talking about the Fourier transform. My understanding was that author proposed that "trick" in context of discrete series for bounded non-periodic functions x(t), y(t).
Instead, what followed was more like an extension to periodic function.
I might add that in a rewrite of the article if more people feel this way.
Blog instantly added to my feedly.