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Some remarks. The series in Eq. 1 of the question: $$y_m = \sum_{k=-\infty}^{\infty}\sum_{n=0}^{N-1}\operatorname{sinc}\left(\frac{Nm}{M} - n - Nk\right)x_n$$ explicitly means this (see this answer to the Mathematics Stack Exchange question: Notation of double-sided infinite sum): $$\begin{align}y_m &= \lim_{K_2\to\infty}\lim_{K_1\to\infty}\sum_{k=-...


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FYI: This was the question I put to the math guys, but here I changed the notation from what might be most conventional to the math guys to one that is more conventional to EEs. (I am using that post as a starting point to sorta exhaustively deal with Olli's question, but in mathematical terms that are easier for me to grok, so i am not exactly following ...


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The indexing is a matter of convention. "Natural" is zero centered, "Computer implementation" is zero based. We are having a big discussion right now over several questions on why your $c_{-5}$ should actually be considered as $(c_{-5} + $c_{5})/2$. You'll find part of the discussion here Convergence of periodic sinc interpolation and the links to the ...


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I'm top-editing this since it answers the question directly. The sinc series is fundamentally a $C/x$, so you can extract as many absolutely convergent series out of it as you want, but what is left over is still only conditionally convergent. Also, you can rescale $x$ and it is still a $C/x$ series. Saying you have a summation to or from infinity is an ...


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It's your observation interval which creates the main problem. Your reasoning based on the Nyquist sampling theorem is ok; of course with a pure sine wave at the exact Nyquist frequency you will have troubles and therefore it's wise to relax the sampling frequency (slightly) above that of Nyquist rate, such 2.2 Hz instead of a strict 2 Hz... So this is one ...


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