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I have a simple question. If I compute N sample values of a single cycle of a discrete sinewave (whose initial phase is zero radians), will the value of the last sample be equal to zero?

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  • $\begingroup$ Note: Stochastic points on waves need not sum to zero if they are not discretized in uniform intervals. $\endgroup$ – MisterGeeky Oct 27 '18 at 5:18
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No. Assuming the period of the signal is N samples since your indexing is zero based the $Nth$ sample will be indexed as $N-1$.

Your signal would be modelled by:

$$ x[n] = A \sin \left( \frac{2\pi}{N}n \right) $$

Thus $x[N]=0$ and $x[N-1] = x[-1] = -x[1]$.

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