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I have just started my first proper course in DSP, and am a little confused about a statement in my textbook. The book states:

"Notice that when the Nyqust-frequency is defined as $\pi/\Delta t$, we will with $\omega_m = 2 \pi m/N \Delta t$ where $m = 0, \pm 1, \pm2, ...$ have $\omega_m \neq \pi/ \Delta t$, unless $N$ is even. If we are working with symmetric functions, it can be wise to use an odd number of sampling points."

I see the logic in the first sentence here, but don't understand how it follows from this that it is wise to use an odd number of sampling points for a symmetric function. This statement is not elaborated upon further. Can anyone explain this logic to me? Why it is wise to use an odd number of sampling points for a symmetric function? If anyone could explain this, I would greatly appreciate it!

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It is because it is symmetric about m = 0. So if you have an odd number of points then you can also sample at +/-1, +/-2, and so on. Thus each of the points has it's counterpart except for zero. This only works with an odd number of points.

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  • $\begingroup$ Thanks a lot! But why exactly doesn't it work with an even number of points? Sorry for asking so much, but this is really new to me! $\endgroup$ – Kristian Dec 9 '13 at 21:15
  • $\begingroup$ Never mind. I got it now :). Thanks a lot again! $\endgroup$ – Kristian Dec 9 '13 at 21:42

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