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Old 08-14-2011, 06:52 AM
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Jess_88 Jess_88 is offline
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Default Unit impulse signal. Evaluating an integral

Hey guys.

I have the following example in my notes but there is no working.
Could someone please explain how to reach to solution?
Is he acutely using integration or is he just looking at the "sift property" and noting values of t0, t1, t2 to come to a conclusion.

Here is the question


The Solution


Sifting property noted earlier in my notes


thanks a lot guys
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Old 08-14-2011, 04:12 PM
someonesdad someonesdad is offline
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It's shifting property, not sifting property. If it was sifting, you'd use it in the kitchen with flour.

The solution is staring you in the face. One way to think of the delta function is that it is a continuous analog of the Kronecker delta. It is often used to evaluate an expression at a particular point. Thus, in the example, the function x is evaluated at t = 4.

Here's the analogy. For a discrete sum using the Kronecker delta (and I'm using the Einstein summation convention),

.

The continuous analog is



Assume the integration is over the real line.
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Old 08-17-2011, 02:13 AM
guitarguy12387 guitarguy12387 is offline
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I know i'm being annoying/stickler... but:

http://mathworld.wolfram.com/SiftingProperty.html
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Old 08-17-2011, 04:36 AM
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Quote:
Originally Posted by guitarguy12387 View Post
I know i'm being annoying/stickler... but:

http://mathworld.wolfram.com/SiftingProperty.html
Absolutely not -- truth is truth. I just learned about the Dirac delta function in the 60's and never heard of the sifting property -- looks like they invented it after I studied it. Gave me a good laugh and I appreciate the education!

Oh, another explanation is that I missed that day in class.
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Old 08-17-2011, 11:16 PM
guitarguy12387 guitarguy12387 is offline
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Hehehe

Was that when frequency was spec'd in CPS instead of HZ?
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Old 08-19-2011, 06:54 AM
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good stuff.
Yeah I was wondering what was going on there. My lecture notes said "Sifting" like 20 times haha.
cheers guys
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