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"...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 infi
by zoomablemind 3y ago
"...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!
- deleted 3y ago[deleted]
- laszlokorte 3y ago> Wouldn't this effectively make frequency 0? 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.
- zoomablemind 3y ago> ...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.