"...You may be wondering - the functions and aren't periodic, how come we can still decompose them into sine/cosine sums? One trick is to set the period to infinity, and compute the series at this limit."
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!