I've seen the plot for Blackman window as so in a bunch of books, as on this website:

enter image description here

But plotting the same equation on Wolfram Alpha yields a different plot:

enter image description here

Why is their graph not centered around 0? And why is their peak at y=1?

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    $\begingroup$ You Wolfram query is wrong $\endgroup$
    – msm
    Oct 30 '16 at 9:56
  • $\begingroup$ SE.DSP wishes you a happy new year 2017, with a kind reminder that your question and its answers may require some action (update, votes, acceptance, etc.) $\endgroup$ Dec 31 '16 at 17:09
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    $\begingroup$ Thanks @LaurentDuval. Action executed. Wish you a happy new year as well! $\endgroup$
    – GrowinMan
    Jan 2 '17 at 22:31
  • $\begingroup$ For some reason literature insists on defining window functions as between 0 and N-1, which I find unhelpful, the sinc function being zero-centred for instance. To make the Blackman window centred on 0 simply turn - 0.5 into + 0.5. $\endgroup$ Dec 21 '18 at 22:29

There is a missing $2\times$ factor inside the second cosine, and you get a centered $201$ point windows with the change of variable $x-100$. See at Wolfram:

$$ 0.42 - 0.5*\cos\left(2\pi\frac{x-100}{200}\right) + 0.08 \cos\left(4\pi\frac{x-100}{200}\right)\,.$$


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