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see it like the screen of a scope.
* it says that a full period (or multiples) of the "signal of interest" should exactly fit into the screen.
(and in case of FFT: just imagine the signal "in the screen" is repeated.
Like taking a screenshot, print out 2 times, and if the "end" of the one exactly fits to the "beginning" of the next)
* it also says that the "width" of the screen should be seen as a number of samples. And the number of samples should be 2^n.
See it like the scope contains 256 samples, or 512 or 1024...
* it also says that the number of full periods should be a prime number. (I´d also avoid "1" and "2").
To keep it simple let´s think about just 8 samples in a window.. and a perfect sine fitting into this window.
Then you get 8 points of the sine, with a distance of 360°/8 = 45°.
Now if you start at 0°, you get sine values at 45°, 90°, 135°, 180°, 225°, ...
but you get "identical values for" (ignoring the "sign")
* 0° and 180° (--> 0)
* 45°, 135°, 225°, 315°... (--> 0.707)
* 90°, 180° (--> 1)
Thus some values are "duplicate" or redundant.
But if you have 3 fullwaves in the screen you get 8 different values along the sine.