I've been getting confused everytime we're graphing a summation with a continuous variable inside. For example, say I want to graph this equation with respect to $f$ ($y$ vertical, $f$ horizontal)

$$ y = 5\sum_{k=0}^\infty \operatorname{sinc}^2 \left(\frac k2 \right) \delta(f-k) $$

How do I account for the continuous variabality of $f$ inside? I know this maps to a comb function multiplied by varying constants, but I don't get how f is dealt with. Doesn't it vary continously with $k$?

  • $\begingroup$ Welcome to Math SE! When you have a minute, please take the tour of the site and look at how to format mathematics here on Math SE. Also, I suggest that you bookmark this very useful MathJax page for quick reference. Cheers! $\endgroup$ – Vee Hua Zhi Nov 9 '18 at 12:11
  • $\begingroup$ I suggest you type out the equation (using MathJax, if possible) and only include pictures only if it is absolutely necessary. $\endgroup$ – Vee Hua Zhi Nov 9 '18 at 12:16
  • $\begingroup$ @Tralala Done. I hope this makes things clearer. $\endgroup$ – M Zein Nov 9 '18 at 12:29
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    $\begingroup$ Hmm, your summation variable $i$ is not mentioned at all in the expression you're summing over ... should it have been $k$? $\endgroup$ – hmakholm left over Monica Nov 9 '18 at 12:34
  • $\begingroup$ @HenningMakholm Oh sorry, yes it should have been k. Wrote I by mistake because it was in the MathJax tutorial. $\endgroup$ – M Zein Nov 9 '18 at 12:37

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