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#1
08-14-2011, 06:52 AM
 Jess_88 Senior Member Join Date: Apr 2011 Location: Australia Posts: 174
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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#2
08-14-2011, 04:12 PM
 someonesdad Senior Member Join Date: Jul 2009 Location: Northwest USA Posts: 1,584

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),

$x_i = \delta_{ij} x_j$.

The continuous analog is

$\int x(t) \delta(t - i) dt = x(i)$

Assume the integration is over the real line.
#3
08-17-2011, 02:13 AM
 guitarguy12387 Senior Member Join Date: Apr 2008 Posts: 359

I know i'm being annoying/stickler... but:

http://mathworld.wolfram.com/SiftingProperty.html
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#4
08-17-2011, 04:36 AM
 someonesdad Senior Member Join Date: Jul 2009 Location: Northwest USA Posts: 1,584

Quote:
 Originally Posted by guitarguy12387 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.
#5
08-17-2011, 11:16 PM
 guitarguy12387 Senior Member Join Date: Apr 2008 Posts: 359

Hehehe

Was that when frequency was spec'd in CPS instead of HZ?
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#6
08-19-2011, 06:54 AM
 Jess_88 Senior Member Join Date: Apr 2011 Location: Australia Posts: 174

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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Give me a lever long enough and a fulcrum on which to place it, and I shall move the world.
-Archimedes

 Tags evaluating, impulse, integral, signal, unit

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