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Sinc^2 as a delta function representation?

  1. Oct 31, 2014 #1
    • OP notified about the compulsory use of the homework template.
    Hi, it's actually not homework but a part of my research.

    I intuitively see that:

    [itex] \lim_{t \rightarrow \infty} \frac{sin^2[(x-a)t]}{(x-a)^2} \propto \delta(x-a) [/itex]

    I know it's certainly true of [itex]sinc[/itex], but I couldn't find any information about [itex]sinc^2[/itex]. Could someone give me a hint on how I could prove it, and find the proportionality coefficient?
     
  2. jcsd
  3. Oct 31, 2014 #2

    Dick

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    A representation of the delta function should have integral 1. Put a=0 and integrate it. You'll find it needs more than just a constant normalization.
     
  4. Nov 1, 2014 #3
    Thanks, so it seems:

    [itex]\lim_{t \rightarrow \infty} \frac{1}{\pi t} \frac{sin^2[(x-a)t]}{(x-a)^2}[/itex]

    does what I want.
     
  5. Nov 1, 2014 #4

    Dick

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    Sounds right.
     
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