unit impulse function

Discussion in 'Homework Help' started by leftbehind5805, Feb 3, 2011.

  1. leftbehind5805

    Thread Starter New Member

    Mar 12, 2010
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    I have a homework assignment where i have to solve several integrals using the unit impulse function. To be honest I am not exactly how to start any of these and the book does not show any examples. Does anyone have a link that shows several examples.

    If there are no link with examples, could some one help me figure out the problem below to help me get started
    ∫δ(T)g(t-T)dT from -infinity to infinity.

    any help is appreciated .
    Thank you
     
  2. narasimhan

    Member

    Dec 3, 2009
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    The basic formula ∫x(t)δ(t-T)dt from -infinity to infinity=x(T)
    I used signals and systems Oppenheim. At first you'll find it difficult but you'll get the hold of it don't worry.
     
  3. Georacer

    Moderator

    Nov 25, 2009
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    This is valid not only from -infty to infty but to any small region around T.
     
  4. narasimhan

    Member

    Dec 3, 2009
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    @Georacer for my equation the any small range around T will do. But for the question that the op posted the range is around zero(since the integration is done with respect to T).

    @op the answer for your integral is g(t)
    hope you could solve the other questions by yourself. if you have any doubts after reading the text do feel free to ask here.
    impulse funtion is very important in signals and systems communication dsp etc. so understanding it is very critical.
     
  5. Georacer

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    Nov 25, 2009
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    Good point. Thanks for the heads-up. But will that mean that the limits of integration are around zero or around t, whatever that is?
     
  6. narasimhan

    Member

    Dec 3, 2009
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    Ya the limits are around zero.

    A simple way to remember is that whatever is inside the δ function should be zero.

    for ∫x(t)δ(t-T)dt the integral is around T

    for ∫δ(T)g(t-T)dT the integral is around zero
     
  7. Georacer

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    Nov 25, 2009
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    Too true... (Does that expression exist?)
     
  8. narasimhan

    Member

    Dec 3, 2009
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    Which one? Both expressions in my previous post are valid and have solution(which is already there in my other post).
     
  9. Georacer

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    Nov 25, 2009
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    My question was purely linguistic: The expression at question is "Too true". :D
     
  10. narasimhan

    Member

    Dec 3, 2009
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    Oh I get it:D.
     
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