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The convolution of two functions with different parameters

  1. Dec 11, 2013 #1
    Hello all,

    What is the result of this (linear) convolution:

    [tex]s(t)\star\delta(\tau-\tau_p)[/tex]

    where s(t) is a continuous signal, δ is the Dirac delta function, and \tau_p is a constant.

    Thanks in advance
     
  2. jcsd
  3. Dec 11, 2013 #2
    Anything convoluted with the Dirac is its self. So give that you've shifted the dirace by tau the result would be s shifted by tau as well
     
  4. Dec 11, 2013 #3
    You mean shifted by tau_p, right? But here the Dirac is a function of tau shifted by tau_p while s(t) is a function of t!! Does this matter?
     
  5. Dec 11, 2013 #4
    Hmmmm I did't notice that the dirac was using tau... I would think that is a typo in the question as it doesnt make sense. However to be fair just cause I haven't seen soemthing doesn't mean it doesnt make sense in some context...

    With convolution the only time I've seen tau used as a varible is with the integral definition of the convolution operation...

    Sorry I guess I should've read the question more carefully :(
     
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