Unit impulse signal. Evaluating an integral

Thread Starter

Jess_88

Joined Apr 29, 2011
174
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 :)
 

someonesdad

Joined Jul 7, 2009
1,583
It's shifting property, not sifting property. If it was sifting, you'd use it in the kitchen with flour. :p

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.
 

Thread Starter

Jess_88

Joined Apr 29, 2011
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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