Comments by "Cheese Business" (@cheesebusiness) on "The Most Important Algorithm Of All Time" video.

  1. 11:40 This is true only for repeating signals (i.e. when a signal segment you have repeats indefinitely). If the portion is solitary (i.e. the rest samples before and after are 0), the spectrum is continuous.
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  2. 12:48 A mistake. The highest distinguishable frequency is N/2. Fundamental x 4 in this case. On the next slide an 8Hz wave is shown with 8 samples. If you take a look closely, you'll see that every sample corresponds to a cosine wave high peak. I.e. an 8Hz cosine wave produces that same signal as a 0Hz "wave" with a non-zero amplitude at the sample time points. What the slide actually shows is that if you try to calculate frequencies higher than N/2, you'll get "ghosts" of lower frequencies (1Hz → 7Hz in that case). Fourier Transform really produces 8 frequency numbers for 8 sample numbers. 4 numbers represent the sine sums, the other 4 represent the cosine sums (of the same frequencies).
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